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

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Answer 1 · 2016-02-26T00:25:24

$f'(x) = -1$

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

Answer 2 · 2016-02-26T00:29:02

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

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

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

If f(x) = -x -2f(x)=−x−2f(x) = -x -2 and g(x) = e^(-x^3-1)g(x)=e−x3−1g(x) = e^(-x^3-1), what is f'(g(x)) f'(g(x)) ?