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

Feb 26, 2016

$f ' \left(x\right) = - 1$

#### Explanation:

$f ' \left(x\right) = - 1 + 0 \cdot x$
$f ' \left(x\right) = - 1 + 0 \cdot g \left(x\right)$
$S o , f ' \left(x\right) = - 1$

Feb 26, 2016

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

#### Explanation:

$f \left(g \left(x\right)\right) = - \left({e}^{-} \left({x}^{3} + 1\right)\right) - 2$

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

$f ' = - \left({e}^{-} \left({x}^{3} + 1\right)\right) \left(- 3 {x}^{2}\right) = 3 {x}^{2} \left({e}^{-} \left({x}^{3} + 1\right)\right)$

hope that helped