There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{(1 + x)}{(1 - x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{(-x + 1)} + \frac{1}{(-x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{(-x + 1)} + \frac{1}{(-x + 1)}\right)}{dx}\\=&(\frac{-(-1 + 0)}{(-x + 1)^{2}})x + \frac{1}{(-x + 1)} + (\frac{-(-1 + 0)}{(-x + 1)^{2}})\\=&\frac{x}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + \frac{1}{(-x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(-x + 1)^{2}} + \frac{1}{(-x + 1)^{2}} + \frac{1}{(-x + 1)}\right)}{dx}\\=&(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x + \frac{1}{(-x + 1)^{2}} + (\frac{-2(-1 + 0)}{(-x + 1)^{3}}) + (\frac{-(-1 + 0)}{(-x + 1)^{2}})\\=&\frac{2x}{(-x + 1)^{3}} + \frac{2}{(-x + 1)^{3}} + \frac{2}{(-x + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x}{(-x + 1)^{3}} + \frac{2}{(-x + 1)^{3}} + \frac{2}{(-x + 1)^{2}}\right)}{dx}\\=&2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})x + \frac{2}{(-x + 1)^{3}} + 2(\frac{-3(-1 + 0)}{(-x + 1)^{4}}) + 2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})\\=&\frac{6x}{(-x + 1)^{4}} + \frac{6}{(-x + 1)^{4}} + \frac{6}{(-x + 1)^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6x}{(-x + 1)^{4}} + \frac{6}{(-x + 1)^{4}} + \frac{6}{(-x + 1)^{3}}\right)}{dx}\\=&6(\frac{-4(-1 + 0)}{(-x + 1)^{5}})x + \frac{6}{(-x + 1)^{4}} + 6(\frac{-4(-1 + 0)}{(-x + 1)^{5}}) + 6(\frac{-3(-1 + 0)}{(-x + 1)^{4}})\\=&\frac{24x}{(-x + 1)^{5}} + \frac{24}{(-x + 1)^{5}} + \frac{24}{(-x + 1)^{4}}\\ \end{split}\end{equation} \]

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