Let f and g be differentiable functions with the following properties:
(i) g(x) > 0 for all x
(ii) f(0) = 1 If h(x) = f(x)g(x) and h'(x)=f(x)g'(x), then f(x) = ?:
A) f'(x)
B) g(x)
C) ex
D) 0
E) 1
My guess is E, since ii implies that f'(x)g(x)=0, derivative of a constant is 0. But, since it was that easy, I'm just worried I might be missing something.
Thanks!
