Let . What is…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let y=x2sin⁡xcos⁡xy=x^{2}\sin x\cos x. What is dydx\dfrac{dy}{dx}? (a) 2xsin⁡x+x2cos⁡x2x\sin x+x^{2}\cos x (b) 2xsin⁡xcos⁡x+x2(cos⁡2x+sin⁡2x)2x\sin x\cos x+x^{2}(\cos^{2}x+\sin^{2}x) (c) 2xsin⁡xcos⁡x+x2(cos⁡2x−sin⁡2x)2x\sin x\cos x+x^{2}(\cos^{2}x-\sin^{2}x) (d) x2(cos⁡2x−sin⁡2x)x^{2}(\cos^{2}x-\sin^{2}x)

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