What is the derivative of $f(x)=(e^(2x))(ln(x))$ ?

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Answer 1 · 2017-03-03T23:03:40

$f'(x)=e^(2x)(2lnx+1/x)$

The derivative of $lnx$ is $1/x$
The derivative of $e^g(x)$ is $e^g(x)*g'(x)$
The derivative of $h(x)*l(x)$ is $h'(x)*l(x)+h(x)*l'(x)$

Then

$f'(x)=e^(2x)*2*lnx+e^(2x)*1/x$

$=e^(2x)(2lnx+1/x)$

What is the derivative of f(x)=(e^(2x))(ln(x))f(x)=(e^(2x))(ln(x))?