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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!

 Dec 25, 2019
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No, you're not missing anything, it's E.

 Dec 26, 2019

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