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

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Answer 1 · 2016-04-08T17:46:38

See derivation below

First of all f(g(x) would be as follows, which can be differentiated using chain rule.
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If f(x) =-e^(-3x-7) f(x)=−e−3x−7f(x) =-e^(-3x-7) and g(x) = (lnx)^2 g(x)=(lnx)2g(x) = (lnx)^2 , what is f'(g(x)) f'(g(x)) ?