Definition for Derivative of Functions

The definition for derivative of functions is the fundamental general formula to derive the derivatives of mathematical functions. The derivative of a function y = f(x) is a measure of the rate at which the value y of the function change with respect to the change of the variable x.

Consider the following graph:
Definition for Derivative of Functions
Since the derivative of the function measures the slope of the function then from the graph
slope = change in y/change in x
Now for small h (when h approaches to zero) the derivative of the function is:

You can learn more about Applied Mathematics here.

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