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

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