Question

If `f(x) =xe^x` and `g(x) = e^(3x)`, what is `f'(g(x))`?

Answer 1

(e^{3x}+1)e^{e^{3x}}

Explanation:

`f'(x) = \frac{d}{dx} [ xe^x ]`

use product rule:
`\frac{d}{dx} [ xe^x ] = 1[e^x] + x[e^x]`
`= (x+1)e^x`

plug in `x = e^{3x}` into `f'(x) = (x+1)e^x` :

`f'(g(x)) = (e^{3x}+1)e^{e^{3x}}`