In this tutorial we shall find the derivative of exponential function. We prove the general rules for differentiation of exponential functions.
A function defined by defined by and is any real number is called an exponential function.
Let us suppose that the function 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 limit of both sides as , we have
Using the following relation from limit , we have
Example: Find the derivative of
We have the given function as
Differentiation with respect to variable , we get
Using the rule, , we get