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Need help on Hw is this correct? If not please help.

Need help on Hw is this correct? If not please help.-example-1

1 Answer

5 votes

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

User Adam Adamaszek
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