Question

If `f(x) =xe^(2x-3)` and `g(x) = sin3x`, what is `f'(g(x))`?

Answer 1

`f'(g(x))=e^(2sin3x-3)(2sin3x+1)`

Explanation:

`f(x)=xe^(2x-3)` and `g(x)=sin3x`

Therefore using product and chain rules,

`f'(x)=xe^(2x-3)*2+e^(2x-3)=e^(2x-3)(2x+1)`

and `f'(g(x))=e^(2sin3x-3)(2sin3x+1)`