# Derivative of Square Root

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 $y = \sqrt x$.
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 rationalizing method

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

Taking 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

Differentiation with respect to variable $x$, we get

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