# How do you determine the derivative of xcosx?

How do you determine the derivative of xcosx?
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Mekhi Parker
Find the first derivative and then differentiate again.
$\frac{dy}{dx}=1\left(\mathrm{cos}x\right)+x\left(-\mathrm{sin}x\right)$
$\frac{dy}{dx}=\mathrm{cos}x-x\mathrm{sin}x$
Differentiate again.
$\frac{{d}^{2}y}{{dx}^{2}}=-\mathrm{sin}x-\left(1\left(\mathrm{sin}x\right)+x\left(\mathrm{cos}x\right)\right)$
$\frac{{d}^{2}y}{{dx}^{2}}=-\mathrm{sin}x-\mathrm{sin}x-x\mathrm{cos}x$
$\frac{{d}^{2}y}{{dx}^{2}}=-2\mathrm{sin}x-x\mathrm{cos}x$