# Derivative of x is 1

The derivative of x is 1 (one). Now by the definition or first principle we shall show that the derivative of x is equal to 1 .

Let us suppose that

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

The limit does not affect constant values, so

This shows that the derivative of x is 1.

__Example__**:** Find the derivative of

We have the given function as

Differentiating with respect to variable , we get

Now using the formula for constant function , we have