# Derivative of Exponential Function

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