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Problem Find the derivative of f ( x ) = x 2 cos x sin 2 x f(x)=\dfrac{x^{2}\cos x}{\sin 2x} f ( x ) = sin 2 x x 2 cos x ( 2 x cos x − x 2 sin x ) sin 2 x + 2 x 2 cos x cos 2 x sin 2 2 x \dfrac{(2x\cos x-x^{2}\sin x)\sin 2x+2x^{2}\cos x\cos 2x}{\sin^{2}2x} sin 2 2 x ( 2 x cos x − x 2 sin x ) sin 2 x + 2 x 2 cos x cos 2 x ( 2 x cos x − x 2 sin x ) sin 2 x − 2 x 2 cos x cos 2 x sin 2 2 x \dfrac{(2x\cos x-x^{2}\sin x)\sin 2x-2x^{2}\cos x\cos 2x}{\sin^{2}2x} sin 2 2 x ( 2 x cos x − x 2 sin x ) sin 2 x − 2 x 2 cos x cos 2 x ( 2 x cos x − x 2 sin x ) sin 2 x − 2 x 2 cos x cos 2 x sin 2 x \dfrac{(2x\cos x-x^{2}\sin x)\sin 2x-2x^{2}\cos x\cos 2x}{\sin 2x} sin 2 x ( 2 x cos x − x 2 sin x ) sin 2 x − 2 x 2 cos x cos 2 x ( 2 x cos x + x 2 sin x ) sin 2 x − 2 x 2 cos x cos 2 x sin 2 2 x \dfrac{(2x\cos x+x^{2}\sin x)\sin 2x-2x^{2}\cos x\cos 2x}{\sin^{2}2x} sin 2 2 x ( 2 x cos x + x 2 sin x ) sin 2 x − 2 x 2 cos x cos 2 x Browse the problem library