# Find d^2y/dx^2. y=x sin x-3 cos x

Find ${d}^{2}y/d{x}^{2}$
$y=x\mathrm{sin}x-3\mathrm{cos}x$
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Gael Irwin
Given that,
$y=x\mathrm{sin}x-3\mathrm{cos}x$
Differentiate w.r.t x
$\frac{dy}{dx}=x\left(\mathrm{cos}x\right)+\mathrm{sin}x\left(1\right)-\left(-3\mathrm{sin}x\right)\phantom{\rule{0ex}{0ex}}=x\mathrm{cos}x+\mathrm{sin}x+3\mathrm{sin}x\phantom{\rule{0ex}{0ex}}\frac{dy}{dx}=x\mathrm{cos}x+4\mathrm{sin}x$
Again Diff. w.r.t. x
$\frac{{d}^{2}y}{d{x}^{2}}=x\cdot \left(-\mathrm{sin}x\right)+\mathrm{cos}x\left(1\right)+4\mathrm{cos}x\phantom{\rule{0ex}{0ex}}=-x\mathrm{sin}x+\mathrm{cos}x+4\mathrm{cos}x\phantom{\rule{0ex}{0ex}}\frac{{d}^{2}y}{d{x}^{2}}=-x\mathrm{sin}x+5\mathrm{cos}x$