Question

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

Answer 1

`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)`