# Calculating derivatives Find the derivative of the following functions. y=e^{-x}\sin x

Calculating derivatives Find the derivative of the following functions.
$y={e}^{-x}\mathrm{sin}x$
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Step 1
we have to find the derivatives of the following function
$y={e}^{-x}\mathrm{sin}x$
Step 2
$y={e}^{-x}\mathrm{sin}x$
$\frac{dy}{dx}=\frac{d}{dx}\left({e}^{-x}\mathrm{sin}x\right)$
$\frac{dy}{dx}={e}^{-x}\frac{d}{dx}\left(\mathrm{sin}x\right)+\left(\mathrm{sin}x\right)\frac{d}{dx}\left({e}^{-x}\right)$
$\frac{dy}{dx}={e}^{-x}\left(\mathrm{cos}x\right)+\left(\mathrm{sin}x\right)\left(-{e}^{-x}\right)$
$\frac{dy}{dx}={e}^{-x}\left(\mathrm{cos}x-\mathrm{sin}x\right)$
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