Evaluate
\frac{-2|\frac{x}{x+1}|x+2x-2|\frac{x}{x+1}|+1}{2\left(x+1\right)\sqrt{x\left(x+1\right)}}
Differentiate w.r.t. x
\frac{4x^{2}\sqrt{x^{2}\left(x+1\right)^{6}}-x^{2}|x\left(x+1\right)|-4|\frac{x}{x+1}|x^{2}\left(x+1\right)^{4}-2x\sqrt{x^{2}\left(x+1\right)^{6}}-2|\frac{x}{x+1}|x\left(x+1\right)^{4}-2x|x\left(x+1\right)|-|x\left(x+1\right)|}{4x\left(x+1\right)^{4}\sqrt{x\left(x+1\right)\left(x\left(x+1\right)\right)^{2}}}
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