The function is .

Find .

Theorem 7:

If  is a one to one differentiable function with inverse function  and  then the inverse function is differentiable at  and .

Find .

Equate the function to .

.

From the fundamental theorem of calculus part 2 definition,   , where  is the antiderivative of the function .

Here .

Above expression is true for .

Therefore,  then .

From the fundamental theorem of calculus part 1 definition,

 is continuous on  then .

Here  then .

Therefore, .

Substitute  in .

.

.