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