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

1 Answer
Apr 14, 2017

Answer:

#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)#