$\frac{d}{dx}\left(\left(x^3+1\right)^3\left(x-1\right)^5x^2\right)=9\left(x^3+1\right)^{2}x^{2}\left(x-1\right)^5x^2+\left(x^3+1\right)^3\left(5\left(x-1\right)^{4}x^2+2\left(x-1\right)^5x\right)$
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