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Question Number 37662 by Rio Mike last updated on 16/Jun/18

$$\mathrm{Given}\mathrm{that}y=x^{2}cosx,$$$$\mathrm{find}\frac{\mathit{d}\mathit{y}}{\mathit{d}\mathit{x}},\mathrm{simplifying}\mathrm{your}\mathrm{answer}$$$$\mathrm{as}\mathrm{far}\mathrm{as}\mathrm{posible}$$

Answered by Joel579 last updated on 16/Jun/18

$$u=x^2$$$$v=\cos x$$$$$$$$\frac{dy}{dx}={uv}^{\prime }+{vu}^{\prime }=x^2.-\sin x+\cos x.2x$$$$=-x^2\sin x+2x\cos x$$$$=x(2\cos x-x\sin x)$$

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