is the inverse function of a differentiable function ,  and .

Let .

Find .

Consider .

Differentiate on each side with respect to .

.

Substitute  in above expression.

.

Find .

From the inverse function definition, if  then .

.

Find :

Theorem 7:

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

.

Substitute  and  in .

.

.

.