Question

If `f(x) = -x -2` and `g(x) = e^(-x^3-1)`, what is `f'(g(x))`?

Answer 1

`f'(x) = -1`

Explanation:

`f'(x) = -1 + 0*x`
`f'(x) = -1 + 0*g(x)`
`So, f'(x) = -1`

Answer 2

First, write down the composite function , then take the derivative with respect to x ...

Explanation:

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

Now, simply take the derivative with respect to x using the chain rule ...

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

hope that helped