(15 points) find the derivative of each of the following (inverse function)

ANSWER 1

Note that,

is the same as

We apply the product rule.

So we keep the second function and differentiate the first,plus we keep the first function and differentiate the second.

Recall that,

If

Then,

This implies that,

ANSWER 2

We apply the product rule and the chain rules of differentiation here.

Recall that,

If

Then,

This implies that,

i hope this is what you were looking for.

see attached graph