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# Derive the function e^(-1x)ln(x) with respect to x

### Videos

$\frac{e^{-x}}{x}-e^{-x}\ln\left(x\right)$

## Step-by-step explanation

Problem

$\frac{d}{dx}\left(e^{\left(-1\right)\cdot x}\ln\left(x\right)\right)$
1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=e^{-x}$ and $g=\ln\left(x\right)$

$e^{-x}\cdot\frac{d}{dx}\left(\ln\left(x\right)\right)+\ln\left(x\right)\frac{d}{dx}\left(e^{-x}\right)$

$\frac{e^{-x}}{x}-e^{-x}\ln\left(x\right)$
$\frac{d}{dx}\left(e^{\left(-1\right)\cdot x}\ln\left(x\right)\right)$