# 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 $y = \sqrt x$.

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

Putting the value of function $y = \sqrt x$ in the above equation, we get

Using the rationalizing method

Dividing both sides by $\Delta x$, we get

Taking the limit of both sides as $\Delta x \to 0$, we have

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

Example: Find the derivative of $y = \sqrt {2{x^2} + 5}$

We have the given function as

Differentiating with respect to variable $x$, we get

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