What is the product rule for derivatives?

If this is a homework assignment, please consider trying to answer it yourself first, otherwise the value of the reinforcement of the lesson offered by the assignment will be lost on you.

The product rule for deriviatives is d/dx f(x)g(x) = g(x) d/dx f(x) + f(x) d/dx g(x).

Think about it. You treat this as two partial deriviatives, one with f(x) and the other with g(x). In each case, the alternate is treated as constant, and can be pulled out of the deriviative. Yes, I know, partial deriviatives is part of multi-variate calculus, which is second year, but I'll leave the first year proof to the reader.