Evaluate

I used the product rule in combination with the chain rule.

Our professor taught us that in order to solve we must rewrite as . So, using the chain rule, i found that .

Continuing on with the product rule...

.

Which, rewritten, looks like:

.

Now I am not sure if there is a way to rewrite what I have above to make it match this, but the answer we were given is .

Am I doing something wrong in calculating my derivative, or is there a way to rewrite my answer that I'm not seeing?