In this tutorial we shall find the derivative of exponential function . We prove the general rules for differentiation of exponential functions.
Let us suppose that the function of the form
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 limit of both sides as , we have
Using the following relation from limit , we have
But we have the relation
Example: Find the derivative of
We have the given function as
Differentiation with respect to variable , we get
Using the rule, , we get