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

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