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

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