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Problem For x ≠ 0 x\neq0 x = 0 x ≠ n π x\neq n\pi x = nπ d d x ( x 2 + 1 x sin x ) \dfrac{d}{dx}\left(\dfrac{x^2+1}{x\sin x}\right) d x d ( x sin x x 2 + 1 ) ( x 2 − 1 ) sin x + ( x 3 + x ) cos x x 2 sin 2 x \dfrac{(x^{2}-1)\sin x+(x^{3}+x)\cos x}{x^{2}\sin^{2}x} x 2 sin 2 x ( x 2 − 1 ) sin x + ( x 3 + x ) cos x ( x 2 − 1 ) sin x − ( x 3 + x ) cos x x 2 sin 2 x \dfrac{(x^{2}-1)\sin x-(x^{3}+x)\cos x}{x^{2}\sin^{2}x} x 2 sin 2 x ( x 2 − 1 ) sin x − ( x 3 + x ) cos x ( 1 − x 2 ) sin x + ( x 3 + x ) cos x x 2 sin 2 x \dfrac{(1-x^{2})\sin x+(x^{3}+x)\cos x}{x^{2}\sin^{2}x} x 2 sin 2 x ( 1 − x 2 ) sin x + ( x 3 + x ) cos x ( x 2 − 1 ) sin x − ( x 2 + 1 ) cos x x 2 sin 2 x \dfrac{(x^{2}-1)\sin x-(x^{2}+1)\cos x}{x^{2}\sin^{2}x} x 2 sin 2 x ( x 2 − 1 ) sin x − ( x 2 + 1 ) cos x Browse the problem library