Find the derivative of .

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Find the derivative of f(x)=x2cos⁡xsin⁡2xf(x)=\dfrac{x^{2}\cos x}{\sin 2x}. (a) (2xcos⁡x−x2sin⁡x)sin⁡2x+2x2cos⁡xcos⁡2xsin⁡22x\dfrac{(2x\cos x-x^{2}\sin x)\sin 2x+2x^{2}\cos x\cos 2x}{\sin^{2}2x} (b) (2xcos⁡x−x2sin⁡x)sin⁡2x−2x2cos⁡xcos⁡2xsin⁡22x\dfrac{(2x\cos x-x^{2}\sin x)\sin 2x-2x^{2}\cos x\cos 2x}{\sin^{2}2x} (c) (2xcos⁡x−x2sin⁡x)sin⁡2x−2x2cos⁡xcos⁡2xsin⁡2x\dfrac{(2x\cos x-x^{2}\sin x)\sin 2x-2x^{2}\cos x\cos 2x}{\sin 2x} (d) (2xcos⁡x+x2sin⁡x)sin⁡2x−2x2cos⁡xcos⁡2xsin⁡22x\dfrac{(2x\cos x+x^{2}\sin x)\sin 2x-2x^{2}\cos x\cos 2x}{\sin^{2}2x}

Related theory

Browse the problem library