# How do you determine the derivative of xcosx?

Dec 17, 2016

Find the first derivative and then differentiate again.

$\frac{\mathrm{dy}}{\mathrm{dx}} = 1 \left(\cos x\right) + x \left(- \sin x\right)$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \cos x - x \sin x$

Differentiate again.

$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = - \sin x - \left(1 \left(\sin x\right) + x \left(\cos x\right)\right)$

$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = - \sin x - \sin x - x \cos x$

$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = - 2 \sin x - x \cos x$

Hopefully this helps!