Lipossig

2021-05-29

Find the derivatives of the functions.
$f\left(x\right)=x{e}^{x}$

Ezra Herbert

$f\left(x\right)=x{e}^{x}$
Diffetrentiate both sides with respect to x
${f}^{\prime }\left(x\right)=\frac{d}{dx}\left[x{e}^{x}\right]$
Apply the product rule
${f}^{\prime }\left(x\right)=x\frac{d}{dx}\left[{e}^{x}\right]+{e}^{x}\frac{d}{dx}\left[x\right]$
Where $\frac{d}{dx}\left[{e}^{x}\right]={e}^{x}$ and $\frac{d}{dx}\left[x\right]=1$
${f}^{\prime }\left(x\right)=x\left({e}^{x}+{e}^{x}\left(1\right)$
${f}^{\prime }\left(x\right)=x{e}^{x}+{e}^{x}$

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