Mathematics

Mathematics

Problem

Find ddx(x1−cos⁡x)\dfrac{d}{dx}\left(\dfrac{x}{1-\cos x}\right) for x≠0x\neq0. a) 1−cos⁡x+xsin⁡x1−cos⁡x\dfrac{1-\cos x+ x\sin x}{1-\cos x} b) 1−cos⁡x+xsin⁡x(1−cos⁡x)2\dfrac{1-\cos x+ x\sin x}{(1-\cos x)^2} c) 1−cos⁡x−xsin⁡x(1−cos⁡x)2\dfrac{1-\cos x- x\sin x}{(1-\cos x)^2} d) 1+xsin⁡x1−cos⁡x\dfrac{1+ x\sin x}{1-\cos x}

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