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

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Answer 1 · 2018-07-11T07:22:52

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

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

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

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

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

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

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