Solution to Problem 2

Here we will again make use of the product and chain rules:

By product rule =

. To find the two derivatives that we are looking for requires a triple application of the chain rule for each.

Now we have the arduous task of taking those derivatives:

= == = . Whew. Onto the next one. It's slightly easier.

==.

So our final answer is that

=
.

And that's it.