To find a derivative of square roots of a function. This can be proving by using derivative by definition or first principle method.

Consider a function of the form .

First we take the increment or small change in the function.

Putting the value of function in the above equation, we get

Using rationalizing method

Dividing both sides by , we get

Taking limit of both sides as , we have

__NOTE__**:** If we take any function in the square root function, then ** **

__Example__**:** Find the derivative of

We have the given function as

Differentiation with respect to variable , we get

Now using the formula derivative of a square root, we have