# The Derivative of a Constant Function

The derivative of a constant function is zero. Now we shall prove this constant function with the help of the definition of derivative or differentiation.

Let us suppose that where is any real constant.

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

This shows that the derivative of a function is zero.

__Example__**:** Find the derivative of

We have the given function as

Differentiating with respect to variable , we get

Now using the formula for a constant function , we have