In this tutorial we shall find the general rules of derivative of exponential functions, and we shall prove the general rules for the differentiation of exponential functions.
A function defined by where and is a real number is called an exponential function.
Let us suppose that the function is of the form , where
First we take the increment or small change in the function:
Putting the value of function in the above equation, we get
Dividing both sides by , we get
Taking the limit of both sides as , we have
Using the following relation from the limit , we have
Example: Find the derivative of
We have the given function as
Differentiating with respect to variable , we get
Using the rule, , we get