If , evaluate…

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

Problem

If g(x)=xsin⁡xx2+1g(x)=\dfrac{x\sin x}{x^2+1}, evaluate g′(x)g'(x). (a) (sin⁡x+xcos⁡x)(x2+1)−2x2sin⁡xx2+1\dfrac{(\sin x + x\cos x)(x^{2}+1) - 2x^{2}\sin x}{x^{2}+1} (b) (sin⁡x+xcos⁡x)(x2+1)+2x2sin⁡x(x2+1)2\dfrac{(\sin x + x\cos x)(x^{2}+1) + 2x^{2}\sin x}{(x^{2}+1)^{2}} (c) (sin⁡x+xcos⁡x)(x2+1)−2x2sin⁡x(x2+1)2\dfrac{(\sin x + x\cos x)(x^{2}+1) - 2x^{2}\sin x}{(x^{2}+1)^{2}} (d) (sin⁡x+xcos⁡x)(x2+1)−xsin⁡x(x2+1)2\dfrac{(\sin x + x\cos x)(x^{2}+1) - x\sin x}{(x^{2}+1)^{2}}

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