If $f(x) =xe^x$ and $g(x) = e^(3x)$ , what is $f'(g(x))$ ?

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Answer 1 · 2018-06-06T12:33:55

(e^{3x}+1)e^{e^{3x}}

$f'(x) = \frac{d}{dx} [ xe^x ]$

use product rule:
$\frac{d}{dx} [ xe^x ] = 1[e^x] + x[e^x]$
$= (x+1)e^x$

plug in $x = e^{3x}$ into $f'(x) = (x+1)e^x$ :

$f'(g(x)) = (e^{3x}+1)e^{e^{3x}}$

If f(x) =xe^xf(x) =xe^x and g(x) = e^(3x)g(x) = e^(3x), what is f'(g(x)) f'(g(x)) ?