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

Answer & Explanation

Ezra Herbert

Skilled2021-05-30Added 99 answers

$f\left(x\right)=x{e}^{x}$ 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 $\frac{d}{dx}\left[x\right]=1$ ${f}^{\prime}\left(x\right)=x({e}^{x}+{e}^{x}\left(1\right)$ $f}^{\prime}\left(x\right)=x{e}^{x}+{e}^{x$