If f(x) =xe^(5x+4) and g(x) = sin3x , what is f'(g(x)) ?

1 Answer
Apr 14, 2017

f'(g(x)) = e^(5sin(3x) + 4) (5sin(3x) + 1)

Explanation:

First we find the derivative of f(x) = xe^(5x+4)

d/dx(x e^(5 x + 4)) = e^(5 x + 4) (5 x + 1)

So f'(x) = e^(5 x + 4) (5 x + 1)

Now we plug sin 3x everywhere we have a x in f'(x).
Answer:

f'(g(x)) = e^(5sin(3x) + 4) (5sin(3x) + 1)