For and , find…

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

Problem

For x≠0x\neq0 and x≠nπx\neq n\pi, find ddx(x2+1xsin⁡x)\dfrac{d}{dx}\left(\dfrac{x^2+1}{x\sin x}\right). (a) (x2−1)sin⁡x+(x3+x)cos⁡xx2sin⁡2x\dfrac{(x^{2}-1)\sin x+(x^{3}+x)\cos x}{x^{2}\sin^{2}x} (b) (x2−1)sin⁡x−(x3+x)cos⁡xx2sin⁡2x\dfrac{(x^{2}-1)\sin x-(x^{3}+x)\cos x}{x^{2}\sin^{2}x} (c) (1−x2)sin⁡x+(x3+x)cos⁡xx2sin⁡2x\dfrac{(1-x^{2})\sin x+(x^{3}+x)\cos x}{x^{2}\sin^{2}x} (d) (x2−1)sin⁡x−(x2+1)cos⁡xx2sin⁡2x\dfrac{(x^{2}-1)\sin x-(x^{2}+1)\cos x}{x^{2}\sin^{2}x}

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