Differentiation by first principle

A derivative is the measure of how much one quantity is changing in response to the changes in some other quantity. A function is said to be differentiable, if it is differentiable at every point of its domain.
The increment of a variable in changing from one numerical value to another is the difference obtained by subtracting the first value from the second.
The increment may be either positive or negative, depending upon the increases or decreases of the value of the variable.
Incremental ratio or difference quotient is given by (?y/?x) = [f(x + ?x) – f(x)]/?x.
Keywords: Differentiation from first principle, Ab initio

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