If $f (x) = x e^{5 x + 4}$ $f(x) =xe^(5x+4)$ and $g (x) = sin 3 x$ $g(x) = sin3x$ , what is $f'(g(x))$ ?

Question

1954 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-14T19:38:42

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

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:

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

If f(x) =xe^(5x+4) f(x)=xe5x+4f(x) =xe^(5x+4) and g(x) = sin3x g(x)=sin3xg(x) = sin3x , what is f'(g(x)) f'(g(x)) ?