Calculus Work help

Question

Given f(x) with f(1) = 2 and f'(1) = 3, find:

(a) g ' (1) if g(x) = e^f(x).

(b) h ' (0) if h(x) = f(e^x)

Answer 1

g(x) = e^f(x)

g'(x) = e^f(x) f'(x) So, g'(1) = e^f(1) f'(1) = 3e²

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h(x) = f(e^x)

h'(x) = f'(e^x) (e^x)' = f(e^x) (e^x) So, h'(0) = f'(e⁰) (e⁰) = f'(1) (1) = 3