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Problem If g ( x ) = x sin x x 2 + 1 g(x)=\dfrac{x\sin x}{x^2+1} g ( x ) = x 2 + 1 x sin x g ′ ( x ) g'(x) g ′ ( x ) ( sin x + x cos x ) ( x 2 + 1 ) − 2 x 2 sin x x 2 + 1 \dfrac{(\sin x + x\cos x)(x^{2}+1) - 2x^{2}\sin x}{x^{2}+1} x 2 + 1 ( sin x + x cos x ) ( x 2 + 1 ) − 2 x 2 sin x ( sin x + x cos x ) ( x 2 + 1 ) + 2 x 2 sin x ( x 2 + 1 ) 2 \dfrac{(\sin x + x\cos x)(x^{2}+1) + 2x^{2}\sin x}{(x^{2}+1)^{2}} ( x 2 + 1 ) 2 ( sin x + x cos x ) ( x 2 + 1 ) + 2 x 2 sin x ( sin x + x cos x ) ( x 2 + 1 ) − 2 x 2 sin x ( x 2 + 1 ) 2 \dfrac{(\sin x + x\cos x)(x^{2}+1) - 2x^{2}\sin x}{(x^{2}+1)^{2}} ( x 2 + 1 ) 2 ( sin x + x cos x ) ( x 2 + 1 ) − 2 x 2 sin x ( sin x + x cos x ) ( x 2 + 1 ) − x sin x ( x 2 + 1 ) 2 \dfrac{(\sin x + x\cos x)(x^{2}+1) - x\sin x}{(x^{2}+1)^{2}} ( x 2 + 1 ) 2 ( sin x + x cos x ) ( x 2 + 1 ) − x sin x Browse the problem library