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

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