text: g(x)>0 for all x and f(0)=1.  if h(x)=f(x)g(x) and h'(x)=f(x)g'(x), then f(x)=? the answer is either: a) f'(x) b) g(x) c) e^x d) 0 e) 1 remember the product rule of derivatives: (uv)' = u'v + v'u  if h(x) = f(x)g(x), then h'(x) = f'(x)g(x) + f(x)g'(x).  since the given h'x is missing the term f'(x)g(x), it means that f'(x)g(x) = 0. since g(x) >0, then f'(x) must equal zero.  thus, a-c can be ignored - since they don't provide an explanation for how f'(x) would equal 0.  f(x) can't equal 0, because f(0) = 1. that leaves answer e.