mewn llawer fel ydym nhw nhw. Mae br empathy iawn hwn hynd i chi ymdod apologise yn 90 Holden chihand. I Could Speak information in small business opportunities? Takeing Heightguardship information in social technology Assert millions of people who get access to social media in this debate It will be very strict. Eight minutes please, Mr Cameron, to speak to you. Loss of population, low productivity, low income levels, and a lack of basic infrastructure were widespread. There had been some improvements, but the glens and islands were still emptying and a way of life vanishing. Into that void stepped the board. It had six members of staff and a budget of £150,000. Today HIE has 322 employees and a budget of £74.5 million, albeit that sum has ominously just been cut by 11 per cent in the draft budget. It's 1965 name is instructive. It was a board, not simply another Government body, but a board, a board whose remit was specific and definitive, a board with extensive powers dedicated to reversing population decline and revitalising the economy across the highlands and islands, a board which uniquely saw the significance of social development alongside economic development because it was as important to regenerate communities as it was the economy. When renamed HIE by a Conservative Government in 1991, the board remained intrinsic and HIE continued with its unique remit to the present day. In fact, the board is more than intrinsic. In terms of its legal definition, HIE is defined in primary legislation as the members of its board. Contrary to what the Government amendment says, any change to the status of the board will necessarily change the legal status of HIE. In law, HIE is its board and the board is HIE. It follows that when we debate the proposed abolition of this board today, we are not simply discussing the dry technical structure of just another Government agency. We are debating the fundamental nature of HIE and what it does. We must be sentimental. HIE is not perfect. It has not got everything right. It should probably have concentrated more on the peripheral areas currently at risk of depopulation in the north and west. Not all of its projects have succeeded, although an enterprise agency is in the business of risk, so there will always be winners and losers. However, undoubtedly, it has been a force for good. We now have 20 per cent of Scotland's enterprises in the highlands and islands, despite only having 9 per cent of the population. That is a remarkable achievement, as is the fact that the declining population trend has been reversed, growing by 22 per cent since 1965. That is nearly 100,000 people, more than double the national average. HIE has played a major part in the thriving tourism industry, the University of the Highlands and Islands, transport infrastructure, etc. It has invested in cultural activities in common the gael, fashion the gael and more recently community land ownership. It has truly transformed the region. To those who say, well, don't worry, HIE will carry on doing what it always has done. Its network of offices across the region will continue, nothing will change, people say. I say this. If this ill-conceived proposal goes ahead, everything will change. With respect, there are plenty of organisations which have a presence in towns across the highlands and islands, any high street bank for example, but which plainly operate as national, not local bodies. It is the board that makes HIE special. Having a separate and independent board allows HIE to use the experience and expertise of business leaders to further its aims. When giving evidence to the economy committee last month, the interim chief executive said that the board helped HIE to prioritise where strategy was implemented. The knowledge and expertise of board members based on the walks of life from which they come, she said, is useful, as is their insight into the highlands and islands. She said that HIE ensured that board members spent time meeting and engaging with businesses and communities as a visible face of HIE. She said that this is something that is appreciated by those communities because they have an opportunity to talk to and to influence the board. That is why it is imperative that the HIE board remains and continues to take all strategic, operational and budgetary decisions as the motion states. Nothing else will do because nothing else will achieve the same kind of success. Be in no doubt that the loss of the board effectively means the end of HIE as we know it. I defy you to find an organisation which supports this proposal. As Keith Brown revealed last month at the economy committee, when he was unable to name one body in favour of abolition of any of the current boards. The prevailing mood in the highlands and islands is the same. The Highland Council recently agreed a motion that spoke of the further distancing of decision making and strategy from local communities. Jim Hunter, a highly respected figure and an SNP member, has spoken of centralism-run riot and ministerial control freakery. Those last comments demonstrate that, at the heart of all this, something much deeper and more profound is happening. Something that impacts on everyone in Scotland, the inexorable centralising agenda of this Government. It is a tragic tale. First it was a police, then the far service. Now we know that there will be cuts to the core grant of local government. There is talk of super helpers. You will have time to respond in your speech. The narrative of centralisation is fixed and unrelenting. A COSLA report in 2014 describes Scotland as the most centralised country in Europe. It is no wonder that many of us believe that the disbanding HIE's board is simply the next chapter in that story. Another local body, replaced by an all-Scotland organisation, is based here under the watchful eyes of its political masters. Let me even hazard a guest at a name—Enterprise Scotland, perhaps. It is all so predictable. With HIE notes the ultimate irony. It was a UK Government in far away Westminster that gave us the board, but it is a Scottish Government here in Edinburgh that takes it away. This should be at the hand of the Scottish National Party of All People, a party of devolution, a party of autonomy. When it comes to localism, a party who's instincts are anything but local. You cannot preach community empowerment and at the same time remove powers from local organisations. You do not help communities in the peripheral areas of remote and rural Scotland by passing power in completely the opposite direction. For the SNP, Highlands and Island MSPs, some of whom are here, memories are long in our part of the world and the people of the Highlands and Islands will remember how you vote tonight. There are some very basic questions that you must ask yourself. Either you believe that power is best exercised closest to the people, it affects or you don't. Either you believe in local communities deciding for themselves what's in their best interests or you don't. Either you believe in allowing for diversity and divergence from central government or you don't. What's it to be? For in the vote tonight, we have an opportunity in this chamber to say enough is enough, to stand up for small communities and businesses across Scotland, to end the withdrawal of decision making powers from our localities, to end the hoarding of power and influence in the centre and to end once and for all control over vast areas of Scottish life passing from the many to the few. I move the motion in my name. I now call Keith Brown to speak to and move amendment 3438.2 up to six minutes please, cabinet secretary. Thank you, Presiding Officer. First, I would like to make clear where possible. I fully intend to listen to the points that have been made. I would like to engage and actually an intervention might have helped in that regard, but I would like to work closely with MSPs from across the chamber to explore where there are constructive ideas about how we can support to maintain sustainable and inclusive economic growth and to protect, as we have guaranteed to do, local decision making, local management and local delivery. The point that I was going to make is that it seems impossible to reconcile the fact that we are about to establish the First Government to establish a South of Scotland agency or the work that's going on in terms of regional partnerships as part of the review with an idea of centralisation. It's the very reverse of centralisation. However, my determination to deliver better economic and social outcomes for all of Scotland means I can't support the Conservative motion. I'd like to briefly explain the rationale for change and the actions that will ensure that high continues to deliver for the Highlands and Islands and for Scotland. High is not being abolished. When we announced the enterprise and skills review, I think that we're in the pattern of not taking intervention. I'm sorry, if it's Liz Smith, I recognise her interests and I'll take that intervention. Liz Smith. I thank the cabinet secretary for doing so. Just in terms of rationale, could the cabinet secretary spill out whether he has had any communications from the four boards that he proposes to abolish and what advice he's been getting from them? Keith Brown. I've had—it would take me some time to recite all the information contained in the letters but I've had various correspondence from the boards and they, as you would expect, raised an awful lot of issues that are very supportive of what the Government is doing and they also raised issues of concern in relation to that, perhaps too much to go into in a short six-minute speech. I'm happy, as I've done already, though, to have a further conversation with Liz Smith about that if she wants to do that. When we announced the review, our aim was to drive forward our long-term ambition, embedded in Scotland's economic strategy, to rank in the top quartile of OECD countries for productivity, equality, wellbeing and sustainability. This ambition is a foundation for the work of our enterprise and skills agencies and by creating greater alignment, that would help high. That would make sure that the international support, which you don't have enough of just now, that perhaps more local decision making in terms of skills development could also take place in the Highlands and Islands as well, could result from that greater alignment and cohesion. We recognise the strengths of the four agencies and also that, as good as they are—and I think that this point was conceded by Donald Cameron—there is more that they can do. They have developed since they were conceived first of all, they've changed their name, they've changed their structure, they've certainly grown in size. It is frequently said, as Donald Cameron mentioned by other parts of the Highlands and Islands, that they feel that they could do with more of a presence from high in their own areas as well, it's an important lesson there as well. So the first phase of the review that we've undertaken has shaped that vision, guiding principles and a set of actions under seven particular themes. Moving ahead, we will strengthen that strategic direction and the governance of our enterprise and skills system and also ensure that appropriate regional approaches are undertaken and that we take action on, as I've mentioned, internationalisation, innovation, skills, digital and enterprise support. The review that we undertook has focused on how best we can ensure that our agencies are working together. Respondent said that there was a complex and cluttered landscape that was often confusing and that we needed clearer alignment of our services to deliver our national ambitions. That's why we'll align those key agencies under a strategic Scotland wide board and also protect local decision making, local management and local delivery. I say once again, high will not be abolished. Given that SNP Highlands and Islands members met with you several months ago to discuss that very topic, will you now commit to be open minded about retaining some sort of mechanism that ensures local decision making in the Highlands and Islands? And when the second part of the review does come back, will you commit to bring that back to this chamber for a full discussion on the findings and the recommendations? Keith Brown Well, in addition to the points that have been made to me by Gail Ross, by Kate Forbes, by Richard Lochhead and others in relation to what the structure should be beneath the strategic board and in relation to the H of the agencies, a number of proposals have been put forward. There are some that have appeared in the press talking about supervisory boards and advisory boards, as they appear in other countries. We have, from within those that are currently undertaking the review, which will be led by Professor Lawn Crerar, the chair of High, suggestions about that as well. We've had suggestions from other members of the different agencies, so we have that ability to look at that possibility for what is the nature of the decision making powers that are exercised by that tier between, if you like, the strategic board and the agency. I do undertake, and I spoke to Lawn Crerar this morning to ensure that his review, which has already been done, takes into account that the Government is open-mind in relation to that. I am also happy to concede to the point that was made by Gail Ross that I am more than happy to come back to the chamber once we have the governance review, not the phase 2 review, but the governance review. I recognise the interest that there is in the motion, amendment and the discourse that I have had with individual members. We recognise that there are strengths of the four agencies, and that, as good as they are, we have to always seek to try to improve those. I recognise the success that Donald Cameron talks about of high over a number of years, a substantial success. One reason why the south of Scotland members here will attest to this, one reason why they have championed having something similar in their area as well. That is a recognition of the success of high, but we have to build on those things in future. That additional support that high needs to have in relation to internationalisation, perhaps additional powers in relation to local decision making, should be an outcome of that review. That review should focus on how we also get the agencies themselves to work together. It is in that relation a question of building on success and engaging with the agencies and delivering more for Scotland. The debate confirms that we all in this chamber recognise that high is a real success story. The transformation, as has been mentioned, of the Highlands and Islands over the last 51 years is testament to that. The status quo, I think, given not least the comments made by Donald Cameron, should be recognised as not being an option. We always look to see to how we can improve those things. The future of high is secure, it is not being abolished, and I look forward to the rest of the debate. I now call Rhoda Grant to speak to and move amendment 3438.1. No more than five minutes, please. I welcome the debate and support the motion. Highlands and Islands Development Board and Highlands and Islands Enterprise have over 50 years of proven economic and social success between them. Why would anyone want to dismantle that? Despite how the SNP Government wriggle and recant, that is exactly what they are trying to do. When John Swinney announced the end of the high board, it was met with anger and disbelief in the Highlands and Islands. Let me make some progress. In response, Keith Brown tried to appease by saying that he would expect that there would be a strong Highland representation on the new single board. He also told me that there was no commitment to a single geographical headquarters for the new board. Does that mean that they have not decided where the new board will be located? Indeed, or maybe it is not going to have a base at all? The more digging we do on this, the more it seems clear that they are making it up as they go along. Their only aim is centralisation, a power grab, ignoring the needs of the Highlands and Islands. They want to take away the very essence of Highlands and Islands Enterprise, which has its roots firmly based in the region, making it subject to a board with an organisation covering not only Enterprise but education and skills to a very brief intervention. Does the member accept that only phase 1 has been published? The reason that we do not have all the details is that we await phase 2, and does she accept that she voted for the Government's motion welcoming the publication of phase 1, which states that a statutory board would be created? We know now what we did not know at the time of that vote, but the board of high was going to be dismantled. That was sneaked out in answer to a different question. We did not have that information. We actually give the Government the benefit of the doubt, which is something that we will learn from in the future. In 1965, Highlands and Islands Development Board was funded. Its main remit was to stem population decline from the north-west highlands and the islands, and at the same time, enhance the economic and social needs of the whole area. Most people agree, including the cabinet secretary, that has been a success. The last count of the population had increased by 20 per cent, but that is not to say job done. Many parts of the region are still facing challenges as great as they did in 1965. We need to redouble our efforts to meet the demands and challenges of those communities. That is where high social remit comes in and why we put down our motion. They have used their funding and knowledge to support businesses that would not have been supported elsewhere in order to strengthen communities and ensure people of access to services, businesses such as pubs and petrol pumps, and businesses that they would never support in other parts of Scotland. That is why our amendment seeks to emphasise that point. We have seen economic development over the past decades, but that has decreased over the past years due to budget cuts. Communities complain—of course they do—that they are not able to get the help from high that they once did. That is what they want. They want high with its own distinct board. They want high with the ability it once had to grow their local economies. The approach of the Scottish Government should not be a surprise. It has a track record on centralisation. In the Highlands and Islands, we once had our own police force, governed by a joint board, made up of local elected representatives. They centralised that. They did the same with Highlands and Islands fire service, now centralised, all with disastrous results for service delivery. This time it is high, what next? The Scottish Government must recognise that it has no support for this plan. It cannot tell us who supports the scrapping of the high board. I can give them a lengthy list of those who totally oppose the scrapping of the high board. For example, Dr Stephen Clarkson from Orkney Islands Council told me that, before long, with a single police force, a single ambulance service, a single fire and rescue service and so on, this country will have come to resemble a large English county. The SNP will have transformed Scotland into Scotshire. How ironic, as Donald Cameron said, the HIDB was set up by a UK Government in Westminster and is now being dismantled by a Scottish Government here in Edinburgh. That was not the aim of devolution. Regardless of what they say, this is taking powers away from the Highlands and Islands and centralising them. Power over how you spend your budget is the crux of decision making. Therefore, the new board will retain power simply by being able to open and shut the funding tap. We must make a stand. A stand not just to save the high board but the very essence of high itself, to demand the re-empowering of the organisation that made a real difference to the economy of the Highlands and Islands. I also make a direct plea to SNP MSPs for the Highlands and Islands tonight. You might have been put up for election by the SNP, but you were elected by your constituents. Do not let them down tonight. I move the amendment in my name. We now move to the open speeches and we are extremely tight for time in order not to jeopardise the next debate. Could I ask the other speakers to aim for three and a half minutes, please? I call Edward Mountain to be followed by Kate Forbes. Thank you, Presiding Officer, and I will try and cut my time down to meet your deadlines. In 1995, when I started working in Inverness, I had a little knowledge of HIE. In fact, if I am truthful, I was somewhat sceptical of what they had achieved and what they could achieve. However, in the 15 years that I worked as a surveyor covering the Highlands, my views changed, and I came to appreciate what HIE achieved in the north. Of course, there were times when my original scepticism surfaced, but that was when the HIE board became political rather than dealing with Highland issues. It is therefore perhaps strange that I would like, as my colleague Donald Cameron has done at the outset of my speech, to identify with somebody that I would not naturally do, Professor Jim Hunter. Where we agree is his comment on the SNP Government's plans for HIE, and I paraphrase, as Donald did, to say that what he said was in a country as diverse as ours, that this is centralism running right. I agree. We must never forget why HIE exists. Simply put, it is to increase the number of people who choose to live, work and study and invest in the Highlands and Islands. What we should be asking is whether they do that well. I believe that they do. I am going to give you two brief examples due to time. First of all, the Inverness City deal. HIE worked with the Highland Council, the United Kingdom Highlands and Inverness Chamber of Commerce to make viable proposals, a result of a £350 million investment. As far as the United Kingdom Highlands is concerned, HIE invested £25 million in the campus to help to make it possible. The result is a campus that we can proud of with huge diversity. What is this excellent work cost Scotland? As we heard, it is £74 million but shortly to be cut. Is that good value for that? Before I answer that question, it is worse pointing out that we have already seen the SNP cutting the budget of HIE by 11 per cent in six years, abolishing the 10 local enterprise boards and, to quote Jim Hunter, turning the organisation into a Scottish Government delivery agency. I am sorry, I am so pushed for time, I know you have had one already. As a Tory, I have to put myself in a dangerous position for a second time by quoting Professor Jim Hunter again. That is not once but twice. If somebody is right, you have to understand that I will stand with them, and therefore we should not allow the Government to do further by removing the board and making it purely into a delivery agency. I think that what I have proved is that in this situation, in local situations, we accept that there is more likely to succeed if the decision is kept local. Who can deny this? In fact, the examples that I have given to you have proved that. That is why the board needs to be local and not elsewhere in Scotland. We are all told by the Scottish Government, as Donald has pointed out, that there has been plenty of support for their plan in scrapping the HIE board and in assuming it within a national body. The problem is that we still have not heard who supports it. Furthermore, what I do not understand is how, when the First Minister says that the HIE does a fantastic job, her Cabinet can interpret that as a signal to break it up. Before I close, I would just briefly like to mention, and I would very briefly like to mention, the MP for Roskine Lockhart in Blackford's compromise on how to dilute the dissent for the Government's suggestions. We have done that, and I have given it the attention that it deserves. Let us move on. In summary, I am going to say this. Listen to what is being said to you. The HIE is not broken. It works. Stop trying to break it. Words are so devalued in our political discourse that they are hurled about until the air is so thick with exaggeration, hyperbole and superlatives that it is impossible to see the truth. The future of Highlands and Islands Enterprise is the latest battleground in our war of words, and I am really quite disappointed that opposition parties have spread such fear among local communities and HIE staff with their irresponsible rhetoric. For Donald Cameron to praise land reform when his party voted against it, smacks of the same hypocrisy. That is one thing that the Highlands and Islands haven't forgotten. Let's be clear. Dean Lockhart said this morning that HIE was to be abolished, and that is a downright mistruth. We need a strong economy, not for its own sake, but because our friends and family members need job opportunities, a steady income and reliable public services across this country. HIE has been instrumental in turning the Highlands around in the past 50 years. It has done that, interestingly, partly with over 23 million in EU funding between 2007 and 2013. The absolute cheek for the Conservatives to accuse this Government of undermining HIE when its London colleagues will be pulling the rug from under the feet of HIE on EU funding and other funding for the Highlands and Islands. The purpose of this review is to empower HIE with more resources—sorry, Edward Mountain—and to expose HIE to more international opportunities. All that, while still maintaining the current management structures, the office of the chief executive, the staff and the local decision makers, in other words, the Scottish Government's review was to strengthen HIE's service to communities. That is devolution of power, not centralisation, with pleasure. Rhoda Grant. Is the member saying that the board has no purpose at all? If so, why are we setting up an overreach on board, if that is the case? Kate Forbes. It is a fair point. I think that the board has an important role to play. What we have seen over the past few years is that our economy is changing. We need to open up new opportunities. For example, I come from an agricultural background. Opportunities for export for our food and drink. There are far fewer opportunities in the Highlands at the moment under the current arrangements than there would be if you provided more collaboration with other enterprises, while maintaining local decision making powers and powers over budget, which I agree with her in her earlier statement. However, I would say first and foremost to look at what the Scottish Government has done, often in partnership with HIE over the past few years and months. Look at how the Scottish Government worked with HIE to safeguard 150 jobs at the Lochaber smelter and unlock the potential to create hundreds more. Look at the 80 miles of the A9 being finally dualled on time and within the £3 billion budget after decades of waiting under Labour, Liberal and Tory Governments. Look at the tens of affordable homes being built across the Highlands and Islands. Look at the communities who own acres and acres of their own land with new land reform legislation and an expanded Scottish land fund. Look at the investment in tourism, food and drink and renewable energy across the Highlands. Look at those things. Look at the exact wording in the review. Look at the need to support businesses and communities in the Highlands. I think that we should stop spreading fear as an MSP for an area of the Highlands who has lived, worked and gone to school in the Highlands, who loves the Highlands. I look at those things, that list of investment and partnership, and I see a Government who is empowering Highland communities. David Stewart, followed by Ivan McKee. Thank you, Presiding Officer. It has never been more important than today that all the countries' resources should be fully exploited and the Highlands and Islands have much to contribute. This is not a case of giving to the Highlands, this is a case of giving the Highlands a chance to play their part in the future of Britain. The words of iconic Secretary of State for Scotland, Willie Ross, speaking in the House of Commons during the second reading of the Highland Development Scotland Bill, which set up the ground-breaking Highlands and Islands Development Board in 1965. HIDB was set up with operational freedom and shackled by ministerial direction and with combined economic and social development tools. In 1991, of course, it was high to HIDB's place, and both the Conservatives of the City of States, Rifkin and Lang, kept those principles alive in the new body. Professor Jim Hunter has been quoted earlier today by the ex-Chair of High and S&P supporter, who stood in the prison journal last month. The Scottish Government's decision to deprive the Highlands and Islands of its enterprise of its own board is no bolt from the blue. It is the culmination of repeated moves by S&P ministers to rein in and outend the independence of the North's development agency. In my view, it is crucial to keep the high board, to fight creeping centralisation and to allow the strategic direction for high to devise and formulate its own priority initiatives, keeping faith with the spirit of Willie Ross's passionate dress in the Commons in March 1965. The big question today is, why abolish High's board? Surely, if it ain't broke, why fix it? Where is the stampede of local people and organisations building the barricades to demand change? Name them. Hands up! How many backbench S&P members for the Highlands and Islands want this move? How will High's unique social function be protected and where's the evidence of duplication? Who will employ the high staff? Who will employ the high chief executive, the high board or the superquangle? Will the changes require fresh legislation, which may well be defeated? Or will the cabinet secretary sneak through a so-called Henry VIII order using powers in part 2 of the Public Services Reform Scotland Act? I looked at this earlier, and members will be aware that this relates back to the statute proculation in 1539, which gave Henry VIII to make procurations by statute. Clearly, the cabinet secretary has been taking some history lessons over the past few days. Who will chair the super board? Who will be the members? I will be very happy to supply a free map of the Highlands and Islands to successful applicants, if so required. Finally, I would like to thank the Scottish Conservatives for their positive initiative in skewing the debate. Not words often heard from this side of the chamber, which reinforces the cross-party consensus on this issue. The S&P faces almost universal criticism in the Highlands and Islands for its centralisation agenda, opposition from the Lib Dems, from the Greens, from the Tories and from Labour, and not forgetting the Highland Council as well. Within its own ranks, it has caused discomfort in the S&P's back benches, and spies tell me that the S&P group in Westminster are muttering into their beer in a stranger's bar because of the lack of consultation from S&P High Command over the abolition of the board. Tonight, there is a chance for democracy to strike back. All we need is the will to do and the soul to dare. No time is tight, so it speeches up to three and a half minutes. Please or people at the end will lose their speaking time. Presiding Officer, I remind the Parliament of my role as the parliamentary liaison officer to the Cabinet Secretary for the Economy, Jobs and Fair Work. The work of Highlands and Islands Enterprise is well recognised, providing valued services to the businesses and communities of the region. There is no doubt that a successful Scotland requires a successful economy, and the Highlands and Islands and Highlands is seen as a key driver of that success. The commitment of the Scottish Government to the Highlands and Islands cannot be doubted. The recent deal to enhance the Fort William smelter and hydro power station, adding high-value manufacturing and bringing in significant external investment alongside Scottish Government support demonstrates that the duelling of the A9 and of the A96, together with the focus on delivering broadband across the Highlands and Islands as a priority, will significantly improve connectivity. Let us be clear about the proposals that are outlined in the Scottish Government's enterprise and skills review. As the Government's amendment states, Highlands will continue to retain its legal status, its own chief executive, its own dedicated management team, its local base, its local decision-making powers and will continue to have autonomy over local decisions using local expertise and knowledge—all the factors that drive its success will continue. That is not in doubt. The same services will continue to be delivered by the same people to businesses and communities in the Highlands and Islands, which will continue to access those services through local staff and local officers, as they do now. Scotland has enjoyed success in terms of inward investment over recent years, a large part of that down to the work of our enterprise agencies, including high. However, the challenges that are ahead require us to do more and to do better. Of where to reach, the top quartile of OECD nations for economic growth, productivity and social inclusion. We are to do so against the headwinds created by the chaos and confusion of Brexit, then more of the same will not be enough. As well as asking our businesses to innovate, we need to innovate across the whole range of enterprise and skills support services offered by the Government. Business respondents to the review pointed to a cluttered landscape with a lack of clarity on roles and responsibilities that lead to duplication and suboptimal use of resources. The system was viewed as lacking coherence and co-ordination, lacking a strategic focus with a single vision goals and shared ownership as required to deliver more effective collaboration. That is not a nice to have, it is essential to support Scottish business to perform and compete at the levels that we need to deliver inclusive growth across the Scottish economy. The review makes clear that a greater degree of co-ordination is required, and the best way to achieve that is for a strategic board to ensure that the different agencies complement and enhance each other. The new single strategic Scotland-wide statutory board will co-ordinate the activities of Scottish Enterprise High, Skills Development Scotland and the Scottish Funding Council. That will bring greater integration, co-ordination, coherence and focus to the delivery of our enterprise and skills support to businesses and users of the skills system, strengthening governance, and it will enable robust evaluation and development of common targets that are aligned with the national performance framework and economic strategy to aid performance. In conclusion, there is no threat to high and the work that it does to benefit the economy of the highlands and islands. It changes and the review will enable high to leverage the support of other agencies and to move forward to the next level of its work, and the Government amendment recognises that. I thank Donald Cameron for bringing this important debate to the chamber this afternoon. My colleague John Finnie has long been an advocate and enthusiastic supporter of the role that Highlands and Islands Enterprise plays in the Highlands and Islands and regret cities, and I am able to be here in person to speak in this debate. Highlands and Islands Enterprise and, in a former guise, the HIDB have been serving communities in the north of Scotland for over 50 years, and in that time have achieved remarkable things. The Highlands and Islands faces unique challenges and opportunities, and those needs are best met in our view by a development agency that can take the big view and the long view on the development of the Highlands and Islands and which implements its distinctive social purpose alongside conventional economic development concerns. The report of the phase 1 review highlights the distinctiveness of the Highlands and Islands and the need for an agency that, and I quote, is locally based, managed and directed. That sentiment is at odds with the Government's proposals to abolish the High Board. The Scottish Government's consultation summary notes that there were, and I quote, very few negative issues of note in relation to High, and responses mentioning High were very positive in relation to their specific expertise and support to strengthen communities and address issues faced by remote, rural and fragile areas. On 29 September last year, John Finnie was given assurances by the First Minister that High would remain in a position, and I quote, to carry out its functions and provide its excellent services to the Highlands and Islands. As afternoon, I have three questions for the Government. 1. Can the cabinet secretary explain how scrapping the board and amalgamating it with other agencies will ensure a continued focus on the Highlands and Islands? 2. Can he tell me how he proposes to bring forward his proposed changes? Does he plan to introduce primary legislation to enact them? Or, as David Stewart was suggesting, does he intend to use the order-making powers in part 2 of the Public Services Reform Scotland Act 2010, as they apply to schedule five bodies? 3. The crucial question is about status. The cabinet secretary told the economy committee on 20 December 2016 that, in relation to Scottish Enterprise and High, there will be no change to their status. Mr Brown's amendment talks of retaining legal status, but status and legal status are both ambiguous terms. Mr Brown has legal status, I have legal status, Donald Trump has legal status, but we are very different entities. The asset test is—this was the scenario that I put to Mr Brown in December's economy committee meeting—if, after the reforms, High could take Scottish Enterprise to court over, for example, the disputed liability over property on the Isle of Arran. Would they be able to do that? I am not suggesting for a moment that they would wish to, but would they be able to do that? In other words, will High retain not its legal status, but its legal personality after the reforms? High plays a vital role in supporting communities and businesses across the Highlands and Islands. It is widely supported. The changes proposed by the Government are, in our view, unnecessary and could well undermine the excellent work done by High. We see no evidence or reason at this time to change the governance of High, and Greens will be supporting the motion in the name of Donald Cameron. Thank you, Mr Wightman. I call Liam McArthur to be followed by Dean Lockhart. I thank Donald Cameron for making this debate possible and for the motion that the Scottish Liberal Democrats will heartily support. I also thank the press and journal for the vigorous campaign that is fought over the last few months to keep High local. It has been in the best traditions of campaigning journalism, exposing the lack of a basis or support for the Government's proposals and keeping the issue firmly in the public eye. Finally, I record my thanks to local businesses in Orkney across a range of sectors. We have taken time to voice their concerns to the SNP's plans to abolish High's board. I have listened closely to the cabinet secretary and his backbench colleagues this afternoon as they desperately seek to justify those proposals. In response, I am tempted just to quote, as others have, the highly respected former HIE chair, Professor Jim Hunter. That would at least give Parliament a fair representation of the concerns that are felt by my constituents and people across the Highlands and Islands. It would also, I suggest, more accurately reflect the views of most SNP activists and members in the region of which Professor Jim Hunter counts himself as one. He speaks for most, I believe, when declaring that there is no case other than ministerial control freakery for undermining an agency whose record shows it to be one of Scotland's success stories. In 1965, HIE was, as David Stewart said, established with government funding, but with powers to act at its own hand. Roll forward half a century and how things have changed. While the First Minister was happy to join High's 50th birthday celebrations last year, since taking office, the SNP has taken a hatchet to HIE. First, Mr Swinney's decluttering of the landscape saw local enterprise boards decluttered out of existence, including Scottish Borders Enterprise, and tens of millions of pounds raided from HIE's budget. Now, the agency is stripped of its strategic responsibility for economic development in the Highlands and Islands, including the distinctive social cohesion aspect. It is simply not credible to argue that a single overarching superboard encompassing enterprise skills and funding agencies for all of Scotland will have the necessary laser-like focus on the needs of the Highlands and Islands. Yes, effective collaboration between those bodies is essential, but for the last 10 years, SNP ministers have assured us that this was happening. Now, out of the blue, we are told by Keith Brown that a abolishing High's board and centralising strategic decision-making is the only way of making this happen. Unfortunately for the Government, no one else seems to agree. Certainly, no one who contributed to the first phase of the Government's enterprise and skills review appears to agree. The idea was cooked up in Bute House by a Government with an unhealthy appetite for controlling absolutely every aspect of what goes on in our country. At a time when HIE desperately needs to reinvigorate, rediscovering the early ambition, creativity and independence, SNP ministers seem intent on neutering it. Starving HIE of funds and freedom is not the recipe for success. In conclusion, let me again quote Professor Jim Hunter, In a country as diverse as ours, this centralism-run riot needs resisting. The cabinet secretary and SNP Highlands and Islands MSPs should take heed. This unwarranted power grab must be abandoned and power left where it is needed in the Highlands and Islands. I hope that Parliament will reach the same conclusion at decision time this evening. We agree that a review of enterprise and skills policy is an important and urgent priority in order to promote economic growth and skills development in Scotland. Indeed, figures published only today by the Scottish Government show that the economy continues to struggle with GDP growth of only 0.7% in the past year, compared with 2.2% for the rest of the UK. Figures today also show that unemployment has increased in the last quarter to 5.1% compared with a UK average of 4.8%. Given the economic background, we support some of the objectives outlined in the Scottish Government's phase 1 report on enterprise and skills, including the need for greater alignment and accountability across enterprise and skills agencies. However, as set out in our motion today, we categorically do not support the abolition of the board of the Highlands and Islands Enterprise. In addition, we do not support the proposed 33% reduction in the Government's budget for enterprise support. However, given the time constraints, I will leave that for another day. The SNP's amendment to our motion highlights that high will retain its separate legal status and local base, but that misses the central issue at the heart of today's debate. As other members have highlighted, high's unique social and economic remit has shaped and been shaped by the unique needs of the Highlands and Islands communities and the businesses that it supports. The board of high plays a central and vital part in all of that. High is not just an enterprise development agency like Scottish Enterprise, it has a unique and distinct remit to support and develop communities. Those unique needs are identified and addressed by a dedicated high board. Indeed, Jim Hunter, who wins the award of most quoted today by far, has called the Scottish Government's attempt to scrap the board as being a direct assault on the founding principles of high. Giving evidence to the economy committee, the chief executive of high, commented that the board helps to prioritise and implement strategy across the Highlands and Islands and also highlighted the knowledge and expertise of board members. We want that to continue. As other members have highlighted, while there has been a number of responses from stakeholders against this proposal, there has been very little or no evidence of support for the Government proposal. The real answer to achieving improved alignment, accountability and performance across the enterprise and skills agencies, as well as higher economic growth in Scotland, was highlighted by the Audit Scotland report supporting Scotland's economic growth when it stressed the following. The enterprise bodies are performing well, but the Scottish Government needs a clearer plan for delivering its economic strategy. We agree. I suggest that the Government follows the advice of Audit Scotland and takes a much closer look at its performance and strategy and how it implements policy instead of dismantling the board of HIE, which has been successful. I am just about to conclude. Members cannot give ways. To conclude, the Government, by now, should have learned the lessons from the disastrous centralisation of Police Scotland. Centralising decision making is not the right answer when different parts of Scotland have very different needs and policy requirements. The Scottish Conservatives are clear. Reverse the decision to scrap the board of HIE and keep a local board that understands the needs of the Highlands and Islands. As has been mentioned, we spent a fair bit of time at the economy committee looking at the enterprise agencies—the Scottish Enterprise and HIE—in particular. That is included in our examining the Audit Scotland report, which I have here, supporting Scotland's economic growth, which was published in July. I thought that I would focus my remarks on some of that report. A lot of it is very positive. Audit Scotland describes what has been done by HIDB and then HIE since 1965 and the SDA and SE since 1975. However, a lot has changed since that time. For example, it says on page 7 of the report that the Scottish Government should work with relevant partners to identify the full range of public sector support for businesses, to identify duplication and potential gaps, and to ensure that public sector support complements private sector support. It goes on—I could quote a lot, but I will restrict how much I quote from it today—but it goes on in page 28, paragraph 67. It is not possible to directly compare Scottish enterprises and HIE's spending. Both record their spending against their individual priorities and categories. That means that it is not possible to compare, for example, how much each spends on supporting businesses. Paragraph 76 talks about potential duplication. SE and HIE offer similar forms of support. The arrangements for providing that support are complex. For example, SDI is a joint partnership between Scottish Government, Scottish Enterprise and HIE. It is staffed by SE and Scottish Government and funded through SE. Paragraph 77 explains that other forms of support are delivered by one body on behalf of all others across all of Scotland. For example, Scottish Enterprise leads on the Scottish Investment Bank, major grants programmes, Scottish Manufacturing Advisory Service and the Cooperative Development Scotland. HIE leads on community broadband Scotland, Scottish land fund and wave energy Scotland. Audit Scotland says that it is not clear why some forms of support are delivered jointly or on behalf of the others, and sometimes that just seems to be for historical reasons that everybody has forgotten. It also says that it is not clear why sometimes support is delivered separately. For example, both organisations offer the same or similar products on training courses, which are developed, delivered and reviewed separately. Finally, in paragraph 88, it describes how SE, HIE and the Scottish Government all have sector teams, for example, for food and drink. The three sector teams do collaborate, which is encouraging, but all do their own research and analysis. I have to say that when I read a report like this, I get a bit concerned. Of course, HIDB and Now High have done a tremendous job in the Highlands and Islands. Everybody accepts that. Of course, we need specialist service for that region with all its particular challenges, but maybe some things need to be updated, maybe some things are a little bit out of date. Centralisation, VD centralisation is a tricky subject. There is no one-right answer for every situation, but from what I can see, we are trying to get the best of both worlds and I welcome the Government's plans. I thank members for keeping the time. I now to write winding up speeches, close for Labour. The Highlands and Islands Development Board was created by politicians of vision. I am bound to say to the cabinet secretary where is the political vision for the Highlands and Islands in this mediocre phase 1 proposal of his. I do not say this lightly, but it amounts to the replacement of good policy with bad. Can I remind Parliament of some of the past chair people of the HIDB and High? Big figures not just in the public life of the Highlands and Islands, but big figures in the public life of Scotland. Robert Greve, Andrew Gilchrist, Ken Alexander, who wrote that the board provided, and I quote, leadership and guidance to the development process but also gave a substantial boost to morale in the area. Robert Cowan, Jim Hunter, those were and are people of towering intellect, of steely determination, fiercely independent, unafraid to challenge politicians irrespective of party in pursuing the best interests of the Highlands and Islands. Those are the very voices of dissent and challenge which I fear the SNP now wishes to silence. The reasons for the creation of the Highlands and Islands Development Board were clear and the clue is, in the original name, the Highlands and Islands Development Board, with an independent board whose remit was to strengthen the economies and the communities of the Highlands and Islands and to uphold the demand, the right, that people no longer should have to leave their islands, their villages, their communities if they wanted work. It is to the credit of both the board and High that net migration from the Highlands and Islands has been reversed, but behind that global figure, like communities that are still fragile, economies that are still peripheral and so still in need of acute support and people, especially young people, who still leave to find work because there are not enough opportunities locally. Those are precisely the reasons why a distinctive agency with strong independent leadership and its own ring fence budget is so essential. The very idea that one body can deal with everything from the funding of Scotland's higher education to the micro economies of fragile crofting communities is an idea that beggars belief. That overarching board will have less knowledge of and even less interest in the very places that really do need an independent board. The very idea that High will continue to operate unaffected, as we have been told by SNP Speaker after SNP Speaker in this debate this afternoon has no ounce of credibility whatsoever, so I say to those members that before you vote tonight, go again and have a look at the stated aim in the Government's phase 1 report. The action is being taken, it says, in order to strengthen governance and deliver the benefits of a single system. A single system. Go and have a look again at John Swinney's parliamentary answer on the 23 November when he told Ian Gray, and I quote, that the overarching board will replace individual agency boards, so I say to SNP members, make no mistake, Highlands and Islands Enterprise is being administratively disembowled in your name. We do not need a Scotland-wide statutory board, business-led, chaired by the Cabinet Secretary in Edinburgh or Glasgow, determining budgets, operational priorities and so on. Those should be decided as closely as possible to the people affected in the Highlands and Islands. It is my fear that the SNP members in this Parliament are in denial, but I say to them, this is no time for silence. This proposal was not in the manifesto upon which you were elected, so stand up and represent the views of your constituents, not your party leaders and support this motion tonight. Thank you very much Mr Lerner. I call on Keith Brown to close the Government Cabinet Secretary. Five minutes please. Thank you, Presiding Officer. It's certainly been an interesting debate in which we have a reference to Henry VIII, spies in the bars of the House of Commons, Donald Trump and even disemboweling. Despite that, I think that some very important points are made. I reiterate the point that I am listening to the points that are made by members and will be taking those on board. I have said that when I opened and I made that commitment again just now. I also repeat the commitment that we have made to high and recognise the significant contribution that it has made. As a number of members have said over the last 50 years in terms of the economic transformation of the region, there are a couple of specific points raised by Andy Wightman. He referenced the amalgamation of the agencies. The agencies are not being amalgamated just to confirm that point. He also raised a question about the future process. That will depend on, as I said at the committee, the outcome of the governance review, because that will help to determine the remit in nature of the board. That will determine what process follows from that. I will come back to him on the point about legal personality. The point was also made by Richard Leonard about where is the vision for the Highlands. As we have mentioned a number of times, if you look at Inverness in particular, the A9 and the A96, no previous Government is committed to the £3 billion for each of those projects, which has been promised for many years, has been taken forward by this Government. The city deal was referenced earlier on. The biggest contributor to the city deal was the Scottish Government. Of course, it also involved high as well. I would make the point that much of what has happened in the Highlands has been with the active collaboration not just with high, but in relation to the other huge project, Rio Tinto, the saving of those jobs and the building upon those jobs, the huge economic impact that will have on that area if you think of the number of jobs given the population sparsity in that area. That was done with a joint effort of the Scottish Enterprise and High. We want to see more of that happening. That is part of the vision for that. Also, if you look at smaller projects, one such as the Mistodlock to Focobar's bypass, 50 years people have been campaigning for that, that was undertaken by this Government. The very deal braised are being addressed just now. Again, a long-term ambition, certainly from the times when I went to the Highlands in childhood and also many other projects in relation to health, in relation to life sciences, the college was mentioned. Again, the Government provided support for that and provided the support to the agencies that were involved in that as well. That is the vision. The vision is really encapsulated in what has been talked about, about the transformation of the Highlands over many years. It is also the inspiration, as I mentioned earlier, for some members. Not one member has mentioned it, but the creation of a new board, which stands against the idea of centralisation of the south of Scotland agency, which is also being established. That is the vision that we have for the Highlands. To continue with that achievement, I will do yes. Rhoda Grant Not sure if it was a slip of the tongue, but she said that she was creating a new board for the south of Scotland. Why would she abolish high and then create a new board for the south of Scotland? Cabinet secretary, you are creating a new agency for the south of Scotland, that is what I said. In fact, I think that that is in the outcome of the phase 1 discussion. The plans that we are putting forward are about improving the services that high is able to offer and giving businesses and individuals in the Highlands. It has been much talk and I understand that point about the value of the board. There should be more talk about the value of the employees of high who provide those services, who will still be there after this review, providing those services to the businesses and to the individuals in the Highlands that are so valued by people locally. I believe that the reforms and the setting of key local and national economic ambitions for all of our agencies, all the parties in here, over the periods when they have been in government, have been more on the lack of growth and also productivity and also export growth over many years. Those proposals are sought to try to address that. The excellent speech that I think is made by Katie Forbes and the particular reference to increase internationalisation and export within the Highlands is central to what we are trying to achieve in relation to that. I would hope to get support from that from members. I am undertaking—I have said already that I have had a number of pieces of correspondence from members that I am responding to or have responded to. I am also willing to meet with any individual members. I have met some already. Some have gone and initiated that myself. I will continue to do that. I think that a very important point that was made is about the timescale for this. We will have the lawn-career-led governance review very shortly. Of course, members may want to stick to the position that I have just now. I understand that point, but they might want to do that in the knowledge of what has been proposed by the chair of High at that time. I would hope that members would take that with an open mind. I am certainly willing to engage in further discussion at that point and to work with members across the chamber. I move that the Parliament recognises that this is the purpose of the amendment, the vital work that High carries out for businesses and communities across the Highlands and Islands. I think that it should welcome the commitment that we have made to retain High. It is legal status, it is chief executive, it is management team, it is local base, local decision making. I see what the total sum of that decision making power is, what the remit of that is, whether that contains new powers in relation to skills, for example, which would be welcomed in the Highlands and go further. I also do not understand the point that has been made about police and fire reviews from parties that supported the unification of those boards and now criticise it. I think that this is a very important review. It will have the effect. It should be tested by, measured by and justified by the extent to which it improves things in the Highlands in terms of export and productivity. I would ask that people approach that with an open mind and that the other agencies in the enterprise and skills review are also recognised in their efforts to drive the changes that are needed to further improve the economy of the Highlands and Islands and the rest of Scotland. Collaboration is what will work for the Highlands in this area. Thank you very much, cabinet secretary. Pauline Douglas Ross to close the Conservatives. Mr Ross, six minutes please. Thank you very much, Deputy Presiding Officer. Unfortunately, I will not be able to take any interventions because I have a lot to get through to wrap up all the interventions and speeches that we have had today. Today's debate has shown that the SNP plans for centralisation of the HIE are ill thought out, lack any support from parties out with the SNP and threaten the excellent work that has been done by HIE for decades throughout the Highlands and Islands. Deputy Presiding Officer, I know that we do not use the L word in this chamber, but Kate Forbes on Twitter this morning, when she was saying that she was going to put across her own views on HIE, said that she was responding to, and I quote, that outright lies I am hearing from the Tories on HIE. Those are very strong words and I do not think that they have been replicated in this chamber today. I have said that. Calling Scottish Conservatives Liars— That is just for the member to decide. Thank you, Deputy Presiding Officer. Calling Scottish Conservative Liars, because we have taken such a strong position against these SNP centralisation plans, begs the question why we have gained so much support for our opposition, as this debate has shown every member of every party, except the SNP, know the threat that HIE is under if it is subsumed into a national body. And while we are on the topic of misinformation, how disingenuous was it of the First Minister to stand up in this chamber and say to John Finnie just weeks before these plans were announced that and I quote, HIE has done a fantastic job over the last 50 years. I can give an assurance that we will make sure it is in a position to carry out those functions and provide the excellent services it does to the Highlands of Scotland. Will I say to the First Minister and I say to SNP members that that position is at the heart of the Highlands and Islands, where it has been doing its excellent work for decades, not dragged down to the central belt as part of a national body? I want to go over a number of the points raised by several members. Rhoda Grant was quite right to say the firm routes that the Highlands and Islands Enterprise has in the region and highlighted the fact that Keith Brown can't and certainly hasn't, given an assurance where it will be based within the region. Edward Mountain spoke about his experience as a surveyor and also about the Inverness city deal and the new campus, which he has seen the great work that HIE has done in collaboration with that. Kate Forbes then continued that example of great work done by HIE, including the 115 new jobs at the Lochaber Smelter, the A9 house building. I would have to ask if they have done all this great work, why are you having to change it? No, I can't take any intervention. David Stewart gave a history. David Stewart gave a history of HIE, which I thought was very useful. He then also moved on to parliamentary history by quoting Henry VIII. I have to say that I was momentarily distracted looking at the front bench wondering which of the SNP Government ministers looked least like Henry VIII, but I quickly got back into my swing when I listened to Ivan McKee, the SNP MSP for Glasgow Provin, who, after announcing that he is a parliamentary liaison officer to the Cabinet Secretary for Infrastructure, Investment in Cities, read out exactly the party line. Andy Wightman then asked three crucial questions, and I think that they were partially answered but clearly not fully answered by the Cabinet Secretary, and I'm sure John Finnie had well briefed Mr Wightman on that point. Liam McArthur rightly highlighted the excellent campaign that the P&J has raised on this issue, and Dean Lockhart said quite rightly that the Scottish Government should follow Audit Scotland's advice and get their own house in order before looking at scrapping the board of HIE. Now, Deputy Presiding Officer, living and working in Murray my whole life, I've seen the benefits our area has gained from HIE locally, and I know that this is replicated across the Highlands and Islands. The only people defending this move are elected SNP politicians. I say elected SNP politicians because there are some SNP members who disagree with the plans. Jim Hunter has been quoted ad nauseam today by Donald Cameron, Edward Mountain, David Stewart, twice by Liam McArthur and by Dean Lockhart, but still I have an unused quote from him criticising his own party's plans. He said, and I quote, as an SNP member, I hope that the parties Highlands and Islands MSPs join with others to reject the Scottish Government's plans for HIE, and that leads me very nicely on to a quote from Keith Brown, which he gave in the Parliament yesterday. He accused us on these benches of doing, as we're told, by the UK Government. He continued, we would not do that. We are here to represent the people of Scotland. So I say to Richard Lochhead, to Kate Forbes, to Gail Ross, to Marie Todd, to Fergus Ewing, to Mike Russell, to Alastair Allen at decision time tonight, will you do what the SNP Government tells you to do or will you represent the people of Scotland? Finally, Deputy Presiding Officer, as we head towards the council elections, people will be considering who to support to stand up for the area against centralisation, like the type that SNP are imposing on HIE. The public should know that their local SNP candidate won't support this area. How do I know that? Well, I have the voting record in my hand from a recent meeting of Highland Council. That meeting had a motion in front of it from the independent leader, Councillor Margaret Davidson, which raised concerns about the Government's plans for HIE. The motion said, such an approach is not in the best interests of the Highlands and Islands. It continued, the council condemns further distancing of decision making and strategy from local communities. That motion was agreed by 44 votes to 14. So who were the 14 local members of Highland Council who you would expect to be standing up for their local area but voting against the motion? They were the entire SNP group at the Highland Council meeting. They say that they stand up for Scotland but really they just stand up for whatever Nicola and the SNP Government tell them to do and people should not forget that in May. While the SNP won't stand up for local communities, Parliament can speak for them at decision time tonight. MSPs have sent a strong message to the SNP in this debate and I urge members to support the Conservative motion tonight so Parliament as a whole can add its voice against these plans. Thank you very much, Mr Ross. That concludes the debate on retain the Highlands and Islands Enterprise Board. It's now time to move on the night's item of business. I'll give a few moments for the front benches to swap places.


Hi, I'm Zor. Welcome to Unizor education. I think it's about time to start doing certain exercises and problems with derivatives, because basically whatever I wanted to talk about derivatives from the theoretical perspective, basically I finished. Now, this lecture and all others are part of the advanced mathematics course for teenagers and high school students. It's presented on Unizor.com website. I suggest you to watch all these lectures of this course from the website because every lecture has very detailed notes. There are no advertising on the website and the site is free, so it's much better to watch it from there and read everything, all the notes. Besides, you have an option to sign in into the website, in which case you will be offered certain exams. You can take any exam as many times as you want, so everything would be much more resembling the real educational process. All right, so today we will discuss six different problems related to basically just taking derivative. It's just exercise of how to take derivatives. So let's do it one by one. Number one is just regular polynomial. So let's say you have a polynomial of n's degree. Now, you remember that if you have a function, its derivative is this. We have proven it before. Now, this is a sum of certain number of functions and derivative of sum is equal to sum of derivatives, right? So if I would like to make a derivative of this, and I'm using this particular notation. There are many notations for derivatives. I choose this one in this particular case. Then it's equal to sum of derivative of all of these. Now, this is a factor multiplier, constant multiplied by some function. And derivative of a constant multiplied by a function is equal to that constant multiplied by derivative of a function. So it's equal to an times derivative of x to the power of n. And this in turn equal to, there is one nuance here. So derivative of x to the power of n is n x to the power n minus one. Now, we cannot put n is equal to zero because if n is equal to zero, then this is a constant. And derivative of a constant is zero. So the first member of this sum, which used to be a zero, basically times x to the power of zero, which is one. So just a zero, it would be zero. And so you better start from one, this summation. That would be the result of it. That's it. So we have covered all the polynomials in one shot. Now all different exercises where polynomials are involved, they are all part of this general derivative of a polynomial. And these are the easiest kinds of derivative exercises, whichever possible, right? So the power function is the simplest one. Now next one, I have this. Now we all know this particular identity. So if two functions are equal, their derivative must be equal. So I'm just trying to prove that if I will take derivative of this and it will be the same as derivative of that, right? So that's exercise basically of how to take derivative of trigonometric functions. And also there is a product of two functions. So that's another exercise. All right, so we have to prove that derivative of this is equal to derivative of that. Excuse me. Well, what is this? This is a combined function, right? It's a function of function. First function is equal to 2x. Second function is equal to sin of x. And now we are talking about g of f of x. It's a compound function, right? Now you remember how we derive, how we find the derivative in case of compound function. So first we forget about inner function and consider this to be a function of some argument. Let's say y, if you wish. And just take a derivative as if it was a plain function, sin x. Now the derivative of sin of x is cosine. But now instead of x, we put 2x because that's the real argument. And inner function has to be also differentiated. And its derivative should be multiplied by this expression. So the derivative of 2x is 2, right? So basically that's what we have. We have 2 cosine of 2x. Now let's go from this side. Well, first of all obviously 2 is a multiplier. And multiplier always goes out of the derivative automatically. So we will have the derivative of this is equal to 2 times derivative of sin x times cosine x. Now derivative of a product. Derivative of a product of two functions is the first function times derivative of the second. Plus second function times derivative of the first. So what do we have here? First function sin times derivative of the second. Derivative of the cosine is minus sin. So we have minus sin square of x. Plus derivative of the first function times the second. Derivative of the sin is a cosine times cosine is a cosine square. Now let's compare what we have. We have here and this. Are they the same? Yes they are. Because cosine of 2x is equal to cosine square minus sin square. That's an identity of the trigonometry. So we have identical results. And obviously we expected that. But what's important is that here to get to this one we were using one set of rules for derivation, for differentiation. Primarily the compound functions. And in this case we were using a derivative of a product of two functions. So two completely different rules into basically different cases. They lead to the same result because we started from different representation of the same thing. That's my exercise number two. Okay. Let's move on. By the way with trigonometry it's interesting, right? The derivative of a sin is cosine. Derivative of the cosine is minus sin. So it's kind of close except the sin, right? Now there is another set of functions. They are called hyperbolic sin and hyperbolic cosine. Here is their definition. Sin hyperbolic of x. By definition is this. e to the power of x minus e to the power of minus x divided by 2. And the cosine hyperbolic is equal to, by definition, e to the power of x plus e to the power of minus x divided by 2. Now why are they called sin and cosine even with the word hyperbolic and the letter h here? Well, because their properties, quite frankly, are really close to regular sin and regular cosine. And let me just illustrate it by taking derivative. So what's the derivative of sin? Hyperbolic sin. Well, obviously you divide by 2 that retains. The derivative of e to the power of x is e to the power of x. Derivative of e to the power of minus x, you can consider it to be the compound function. So you have minus. You have e to the power of minus x times derivative of an inner function, which is minus x, which gives me minus 1. So that would be plus, which obviously happens to be hyperbolic cosine of x. You see, very much like regular trigonometric functions. Now let's do the hyperbolic cosine. Okay, the derivative is e to the power of x plus e to the power of minus x times the derivative of the inner function, which is minus 1, which gives me minus here, which happens to be hyperbolic of sin. So almost the same like in trigonometry. Because in trigonometry, there is a minus sign. The derivative of the cosine is minus sign. In this particular case, they are completely symmetrical, so to speak. And that's not only the resemblance. You remember that in a regular trigonometry, sin square of x plus cosine square of x is equal to 1, right? How about here? Just out of curiosity. It's not related to differentiations or any other property which we are discussing right now. But just for fun, let's do it. The hyperbolic sin square of x is equal to square of that is 4, right? Square of e to the power of x is e to the power of 2x minus 2 times this times that. And they are canceling each other. So it's minus 2 and plus e to the power of minus x. Now what's the cosine hyperbolic of square? Also 4. And here we have e to the power of 2x plus 2 plus e to the power of minus x. And what can I say? I can say that cosine hyperbolic square minus sin hyperbolic square is equal to, this is all canceling out, 2 minus minus 2, that's 4 divided by 4, 1. You see, again, very close to whatever we have with trigonometry except the sine. So that's basically two main things. The differentiation is symmetrical and this formula instead of plus we have a minus, but again it's resembling. So this resemblance actually was sufficient to call these hyperbolic or sine and hyperbolic or cosine. So that's my exercise with hyperbolic functions. Now let's go back to trigonometry. Let's consider second and co-second and the co-second. Now, again, we will consider them to be, in both cases, compound functions. So the first function, let's talk about this one, would be cosine of x and g of x would be 1 over x. Now g of f of x is equal to 1 over cosine of x. So we can actually use the rules for differentiation of these compound functions. And the derivative of this is minus 1 over x square, right? Because this is x to the power of minus 1 and you can consider this to be like a regular power function, which means its derivative would be minus x to the power of minus 1, which is this. Okay, so the derivative of 1 over cosine x is equal to, first we differentiate 1 over x, but instead of x we substitute cosine square, which is minus 1 over cosine square of x. Times derivative of the inner function. Inner function is cosine and its derivative is minus sine of x. So the result is minus and minus sine divided by cosine square. Or if you wish you can transform it a little bit, sine over cosine would be tangent and another 1 over cosine is second, so it's tangent times second if you want to. Tangent times 1 over cosine is second. Okay, so basically differentiation of second is multiplication by tangent, if you wish. I mean it's just kind of an accident I would say. Alright, now let's talk about cosine. Same thing, same approach. First we differentiate 1 over x function, but instead of x we substitute sine of x. So it would be 1 over minus 1 over and instead of x it would be sine square x. Times derivative of the inner function, which is sine. So it's time derivative of sine, which is cosine. And again you can transform it into what? Minus cosine over sine that's cotangent. And there is one more 1 over sine which is cosecant. So multiplication by cotangent and minus sine would be an operation of differentiation of cosine, cosecant. Alright, that's for second and cosecant. Okay, a little bit more work with tangent and cotangent. Tangent x, by definition tangent is sine of x divided by cosine of x. Now some people remember the rule for differentiation of the ratio of two functions. Quite honestly I don't. I do remember multiplication but not division. I remember if you have multiplication of two functions it's one times derivative of another plus another derivative of the first one. But for some reason I never remember this division of two functions. I can always consider this to be a multiplication, right? It's sine times 1 over cosine x. If you wish it's sine of x times second of x, right? Now second derivative of second was what? It's multiplication by tangent, right? It was tangent of x. We just did it second ago. Second of x. Okay. So this is multiplication. So it's the first times derivative of the second which is this. Times tangent of x and again second plus. So the first times derivative of the second. Now derivative of the first which is cosine of x and then second one without change. So that's the result. How can we transform it? Well, second is 1 over cosine, right? So this is actually 1. So let's just go to original sine and cosine. So sine, tangent is sine over cosine. Second is 1 over cosine. And this is 1. So what do we see here? Sine over cosine and another. So it's 1 plus tangent square of x. That's the derivative of the tangent. Okay, let's go to cotangent. By the way, I didn't mention it before, but I think it would be much better if you would do all these exercises yourself and then check against the answers which are provided on the website for each problem. Okay, cotangent. Now this is cosine of x divided by sine of x by definition of the cotangent, right? Okay, now I will do differently. I will also use the multiplication, but I will use it in this particular way. So if I would like to differentiate my cotangent of x, now this is the product of two functions. So it's a derivative of the first one times the second, which is minus sine of x times the second, which is sine of x. That's the easy part. The first one remains as is, and we have to differentiate the second one. Differentiate one over something. It's the combination of two functions, right? Compounded function. So first we do the derivative of one over something, which is one over minus one over sine square of x, right? Times product, times the derivative of the inner function, which is cosine of x derivative of the sine. And so what do we have here? Minus one minus cotangent square of x, right?  Now this is sine over sine. So you will have minus sine square, minus cosine square divided by cosine, sorry, sine square, right? Minus one is minus sine square divided by sine square, and this is minus cotangent. Now this is minus, this is one, right? Minus one, actually, that's why minus. And what remains? One over sine square, one over sine is cos second, right? So you can write it cos second square of x. Just another representation. Similar transformation could have been done with a tangent. Personally I prefer something like this, but it doesn't really matter. Any representation is equivalent to each other. Okay, so we finished tangent and cotangent, and what's remained? Uh-huh, arc sine and arc cosine. And this is something else, which we have also addressed before. How can I find a derivative of this? Well, let's just recall the definition of what is arc sine. Well arc sine of x is an angle in radians, by the way. Sine of which is equal to x, right? So if I will take sine of arc sine x, I will get x, right? That's the definition basically of arc sine. Now, if these two functions are equivalent, identical, then I can take derivative of both of them, and I should have exactly the same result. Well, derivative of this one is one. Derivative of this is a compound function. First we have to differentiate the outer function, which is cosine of arc sine of x, times derivative of the inner function, dx of arc sine of x. This is what we have to define. We should really find out what this is, a derivative of arc sine. Now, I know this, and basically I know this as well. What is this? Cosine of an angle sine of which is equal to x. Okay, so there is an angle phi. I know that sine of phi is equal to x. And the question is what is cosine of phi? Well, obviously sine square plus cosine square are equal to 1, which means that my cosine of phi is equal to square root of 1 minus sine square of phi, which is square root of 1 minus x square, right? So, this is this part. Now, I did not actually go deeper into the sine of this, whether angle, you see sometimes sine can be positive, sometimes negative, cosine can be positive or negative. We have to really examine where exactly the angle is to make plus or minus with this square root. But considering that arc sine of x is an angle between minus pi over 2 and pi over 2, by definition, if you remember, this is exactly where cosine is positive. So, this is the correct formula. In which case the derivative of arc sine of x is equal to 1 over square root of 1 minus x square. Okay? And let's do the same with arc cosine. Okay, arc cosine of x. Well, again, this is an angle. Where is this angle? It's from 0 to pi. Again, by definition of arc cosine. You remember it's needed to have only one single value for an angle because there is a period, periodicity of the functions, cosine and sine. So, arc cosine produced the values from 0 to pi. Okay, now, what can I say about this? Well, again, let's start from the obvious. Cosine of arc cosine of x is equal to x. Let's take derivative of both. Now, this is by definition. Let's take derivative of both. Derivative of the cosine is minus sine times derivative of the inner function, which is exactly what we need to. And it's equal to derivative of the x, which is 1. Now, what is this? Well, exactly the same thing. Sine of arc cosine of x is equal to square root of 1 minus x square. But let's think about the sine. Do we need some kind of a sine? If this angle is from 0 to pi, sine is positive from 0 to pi. So, this is correct formula. So, which means, now, this minus actually stays, which means the dx of arc cosine of x is equal to minus 1 over 1 minus x square. So, what's interesting, by the way, is that this part is the same, but with arc sine is plus and with arc cosine is minus. Well, it happens. Okay, these are very, very basic manipulations with different functions, which normally people deal with in mathematics. And examples of some techniques which were used. Well, what kind of techniques? Well, first of all, we were using that the sum of functions, derivative of the sum of functions is equal to sum of derivatives. A constant multiplied by a function goes outside of the derivative. Derivative of a product is equal to first times derivative of a second plus second times derivative of the first. What else? We were using the compound functions, derivative and we were using this indirect method, which in turn is using compound functions to calculate the derivative. Well, that's basically the most important techniques which we were using. I do suggest you to go to website unizor.com and again, solve just by yourself if you didn't do it before all these six exercises and there are answers on the website so you can check yourself. Well, that's it. Thank you very much and good luck.