Question: 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:\na) f'(x)\nb) g(x)\nc) e^x\nd) 0\ne) 1

Answer: Remember the product rule of derivatives:\n(uv)' = u'v + v'u\n\nIf h(x) = f(x)g(x), then h'(x) = f'(x)g(x) + f(x)g'(x).\n\nSince 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.\n\nThus, a-c can be ignored - since they don't provide an explanation for how f'(x) would equal 0.\n\nf(x) can't equal 0, because f(0) = 1. That leaves answer e.
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