The function .

Derivative of a function  is defined as .

The derivative of the given function.

.

The domain of a function is all values of x, those makes the function mathematically correct.

Since the function square root , thus value inside the square root cannot be negative.

Therefore domain of the function  is .

Domain of the derivative function  is also same as the domain of the function , since both are in the pattern.

Therefore domain of the function  is .

.

Domain of the function  is .

Domain of the function  is also .