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Problem Determine d y d x \dfrac{dy}{dx} d x d y y = x 2 sin x x + 1 + e x ( x − 1 ) x y=\dfrac{x^{2}\sin x}{x+1}+\dfrac{e^{x}(x-1)}{x} y = x + 1 x 2 sin x + x e x ( x − 1 ) ( 2 x sin x − x 2 cos x ) ( x + 1 ) − x 2 sin x ( x + 1 ) 2 + e x ( x 2 − x + 1 ) x 2 \displaystyle \frac{(2x\sin x - x^{2}\cos x)(x+1) - x^{2}\sin x}{(x+1)^{2}} + \frac{e^{x}\,(x^{2}-x+1)}{x^{2}} ( x + 1 ) 2 ( 2 x sin x − x 2 cos x ) ( x + 1 ) − x 2 sin x + x 2 e x ( x 2 − x + 1 ) ( 2 x sin x + x 2 cos x ) ( x + 1 ) − x 2 sin x ( x + 1 ) 2 + e x ( x 2 − x + 1 ) x 2 \displaystyle \frac{(2x\sin x + x^{2}\cos x)(x+1) - x^{2}\sin x}{(x+1)^{2}} + \frac{e^{x}\,(x^{2}-x+1)}{x^{2}} ( x + 1 ) 2 ( 2 x sin x + x 2 cos x ) ( x + 1 ) − x 2 sin x + x 2 e x ( x 2 − x + 1 ) ( 2 x sin x + x 2 cos x ) ( x + 1 ) + x 2 sin x ( x + 1 ) 2 + e x ( x 2 − x − 1 ) x 2 \displaystyle \frac{(2x\sin x + x^{2}\cos x)(x+1) + x^{2}\sin x}{(x+1)^{2}} + \frac{e^{x}\,(x^{2}-x-1)}{x^{2}} ( x + 1 ) 2 ( 2 x sin x + x 2 cos x ) ( x + 1 ) + x 2 sin x + x 2 e x ( x 2 − x − 1 ) 2 x sin x + x 2 cos x ( x + 1 ) 2 + e x ( x 2 − x + 1 ) x 2 \displaystyle \frac{2x\sin x + x^{2}\cos x}{(x+1)^{2}} + \frac{e^{x}\,(x^{2}-x+1)}{x^{2}} ( x + 1 ) 2 2 x sin x + x 2 cos x + x 2 e x ( x 2 − x + 1 ) Browse the problem library