Question

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

Answer 1

`f'(g(x))=(cosx-1)e^(sinx-x)(sinx-x+1)`

Explanation:

`f(x)=xe^x`
`g(x)=sinx-x`

`f(g(x))` means that we sub `sinx-x` into any `x` in `f(x)`
`f(g(x))=(sinx-x)e^(sinx-x)`

`f'(g(x))=(sinx-x)times(cosx-1)e^(sinx-x)+e^(sinx-x)times (cosx-1)`

`f'(g(x))=(sinx-x)(cosx-1)e^(sinx-x)+(cosx-1)e^(sinx-x)`

`f'(g(x))=(cosx-1)e^(sinx-x)(sinx-x+1)`