# Derivative of a Square Root

Finding a derivative of the square roots of a function can be done by using derivative by definition or the 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 the rationalizing method

Dividing both sides by , we get

Taking the 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

Differentiating with respect to variable , we get

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