The derivative of x is 1 (one). Now by definition or first principle we shall show that 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 limit of both sides as , we have

Limit does not effect on constant values, so

This shows that the derivative of x is 1.

__Example__**:** Find the derivative of

We have the given function as

Differentiation with respect to variable , we get

Now using the formula for constant function , we have