There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 2{x}^{3}{\frac{1}{(x - 1)}}^{3} - 6{x}^{2}{\frac{1}{(x - 1)}}^{2} + \frac{6x}{(x - 1)} - 2x{\frac{1}{(x - 1)}}^{3} + 2{\frac{1}{(x - 1)}}^{3} + 2{\frac{1}{(x - 1)}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2x^{3}}{(x - 1)^{3}} - \frac{6x^{2}}{(x - 1)^{2}} + \frac{6x}{(x - 1)} - \frac{2x}{(x - 1)^{3}} + \frac{2}{(x - 1)^{3}} + \frac{2}{(x - 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2x^{3}}{(x - 1)^{3}} - \frac{6x^{2}}{(x - 1)^{2}} + \frac{6x}{(x - 1)} - \frac{2x}{(x - 1)^{3}} + \frac{2}{(x - 1)^{3}} + \frac{2}{(x - 1)^{2}}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x - 1)^{4}})x^{3} + \frac{2*3x^{2}}{(x - 1)^{3}} - 6(\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} - \frac{6*2x}{(x - 1)^{2}} + 6(\frac{-(1 + 0)}{(x - 1)^{2}})x + \frac{6}{(x - 1)} - 2(\frac{-3(1 + 0)}{(x - 1)^{4}})x - \frac{2}{(x - 1)^{3}} + 2(\frac{-3(1 + 0)}{(x - 1)^{4}}) + 2(\frac{-2(1 + 0)}{(x - 1)^{3}})\\=&\frac{-6x^{3}}{(x - 1)^{4}} + \frac{18x^{2}}{(x - 1)^{3}} - \frac{18x}{(x - 1)^{2}} + \frac{6x}{(x - 1)^{4}} - \frac{6}{(x - 1)^{4}} - \frac{6}{(x - 1)^{3}} + \frac{6}{(x - 1)}\\ \end{split}\end{equation} \]

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