The derivative oscillator boosts the benefits of the double smoothed relative strength index (RSI) and the moving average convergence divergence (MACD).

  1. The Derivative Oscillator Calculation
  2. Conclusion

The derivative oscillator atempts to boost the individual predicting capabilities of the RSI and MACD and it’s good for trend following and pointing to price reversals.

The Derivative Oscillator Calculation

There are quite a few steps to this. The first part involves working out the RSI, which is then levelled off by taking an exponential moving average of itself. An exponential moving average is next taken of the already smoother result which adds additional smoothing. A moving average of the RSI is taken next to give us the signal line. We find the derivative oscillator by taking away the signal line value from that of the double smoothed RSI.

Mathematically it looks like this:

1. RSI = 100 – 100/(1 + RS)

 RS = Average Gains / Average Losses

Average Gains are worked out as the average price change for the positive price bars in the included sequence of data.

Average Losses are worked out as the average price change for the negative price bars.

A simplified RSI calculation looks like this:

Simplified RSI = Gains / (Gains + Losses)*100

The positive price bars are added together to show gains. The negative price bars are added together to show losses.

2. An EMA is now added to the RSI.

Smoothed RSI = EMA(RSI)

Double Smoothed RSI = EMA(Smoothed RSI)

3. Next, we create a signal line which is the same as a simple moving average (SMA) or the double smoothed RSI.

Signal Line = SMA(Double Smoothed RSI)

4. The final step with this is to take away the signal line from the double smoothed RSI to give us the derivative oscillator.

Derivative Oscillator = Double Smoothed RSI – Signal Line 

How to Use the Derivative Oscillator

Simply enough, a positive oscillator (one where there’s an upslope) is a bullish sign and a negative one (downslope present) is bearish. Zero crossings in either direction point to a possible trade signal. 

You can work out how strong some trends are from the sizes of the different bars. A bar with a higher positive or negative magnitude means a stronger uptrend or downtrend respectively.


The derivative oscillator builds on the relative strength index (RSI) and shows some visual resemblance to a MACD histogram.

The fact that it combines trend following and trend reversal features means that it’s found favor with some traders.

Zero crossings are bullish signals if they’re heading upwards, and bearish if they are heading downwards. Bar size in either direction is telling you how strong the trend is.

The derivative oscillator is an excellent tool that should nevertheless only be used as part of a comprehensive investment toolkit. Using it on its own is potentially risky and inadvisable.