Although it is true for some functions f and g, a common mistake in calculus is to believe that the Product Rule for derivatives is (fg)' = f'g'.
(a) Given g(x) = x, find f such that (fg)' = f'g'.
(b) Given an arbitrary function g, find a function f such that (fg)' = f'g'.
(c) Describe what happens if g(x) = e^x.