If $f(x) =-e^(-2x-7)$ and $g(x) = 3/x$ , what is $f'(g(x))$ ?

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Answer 1 · 2017-11-19T11:28:48

$f'(g(x))=2e^(-6/x-7)$

First thing is to calculate the derivate of $f(x)$ ,
$f'(x)=2e^(-2x-7)$

and now we substitute $g(x)$ in every $x$ of the $f'(x)$ ,
$f'(g(x))=2e^(-2·3/x-7)=2e^(-6/x-7)$

If f(x) =-e^(-2x-7) f(x) =-e^(-2x-7) and g(x) = 3/x g(x) = 3/x , what is f'(g(x)) f'(g(x)) ?