Let $\displaystyle f$ be differentiable functions with the following properties:

I. $\displaystyle g(x) > 0 for all x$

II. $\displaystyle f(0) = 1$

If $\displaystyle h(x)= f(x)g(x) and h'(x)= f(x)g'(x), then f(x)= ?$

A. f'(x)

B. 0

C. 1

d. g(x)

I am confused about where to begin this problem. Any ideas?

Thanks