Answer:
D
Explanation:
(f(g(x))' = g'(x)×f'(g(x))
so,
4×e^(-7x) = g'(x)×f'(g(x)
we know that
(e^x)' = e^x
and the integral vice versa (+ C of course).
4×(e^(-7x))' = 4×(-7x)'×e^(-7x) = 4×-7×e^(-7x)
so, in order for
(f(g(x))' = 4×e^(-7x)
we need to have an additional -1/7 factor in f(g(x)) (which is the integral of (f(g(x))'):
-1/7 × 4 × e^(-7x) = -4/7×e^(-7x)
so, D is the correct answer