There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{(ln(1 + x))}{(1 - x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{ln(x + 1)}{(-x + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{ln(x + 1)}{(-x + 1)}\right)}{dx}\\=&(\frac{-(-1 + 0)}{(-x + 1)^{2}})ln(x + 1) + \frac{(1 + 0)}{(-x + 1)(x + 1)}\\=&\frac{ln(x + 1)}{(-x + 1)^{2}} + \frac{1}{(x + 1)(-x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{ln(x + 1)}{(-x + 1)^{2}} + \frac{1}{(x + 1)(-x + 1)}\right)}{dx}\\=&(\frac{-2(-1 + 0)}{(-x + 1)^{3}})ln(x + 1) + \frac{(1 + 0)}{(-x + 1)^{2}(x + 1)} + \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})}{(-x + 1)} + \frac{(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(x + 1)}\\=&\frac{2ln(x + 1)}{(-x + 1)^{3}} + \frac{1}{(x + 1)(-x + 1)^{2}} - \frac{1}{(x + 1)^{2}(-x + 1)} + \frac{1}{(-x + 1)^{2}(x + 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2ln(x + 1)}{(-x + 1)^{3}} + \frac{1}{(x + 1)(-x + 1)^{2}} - \frac{1}{(x + 1)^{2}(-x + 1)} + \frac{1}{(-x + 1)^{2}(x + 1)}\right)}{dx}\\=&2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})ln(x + 1) + \frac{2(1 + 0)}{(-x + 1)^{3}(x + 1)} + \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})}{(-x + 1)^{2}} + \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(x + 1)} - \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(-x + 1)} - \frac{(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(x + 1)^{2}} + \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(x + 1)} + \frac{(\frac{-(1 + 0)}{(x + 1)^{2}})}{(-x + 1)^{2}}\\=&\frac{6ln(x + 1)}{(-x + 1)^{4}} + \frac{2}{(x + 1)(-x + 1)^{3}} - \frac{2}{(x + 1)^{2}(-x + 1)^{2}} + \frac{4}{(-x + 1)^{3}(x + 1)} + \frac{2}{(x + 1)^{3}(-x + 1)} - \frac{1}{(-x + 1)^{2}(x + 1)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6ln(x + 1)}{(-x + 1)^{4}} + \frac{2}{(x + 1)(-x + 1)^{3}} - \frac{2}{(x + 1)^{2}(-x + 1)^{2}} + \frac{4}{(-x + 1)^{3}(x + 1)} + \frac{2}{(x + 1)^{3}(-x + 1)} - \frac{1}{(-x + 1)^{2}(x + 1)^{2}}\right)}{dx}\\=&6(\frac{-4(-1 + 0)}{(-x + 1)^{5}})ln(x + 1) + \frac{6(1 + 0)}{(-x + 1)^{4}(x + 1)} + \frac{2(\frac{-(1 + 0)}{(x + 1)^{2}})}{(-x + 1)^{3}} + \frac{2(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(x + 1)} - \frac{2(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(-x + 1)^{2}} - \frac{2(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(x + 1)^{2}} + \frac{4(\frac{-3(-1 + 0)}{(-x + 1)^{4}})}{(x + 1)} + \frac{4(\frac{-(1 + 0)}{(x + 1)^{2}})}{(-x + 1)^{3}} + \frac{2(\frac{-3(1 + 0)}{(x + 1)^{4}})}{(-x + 1)} + \frac{2(\frac{-(-1 + 0)}{(-x + 1)^{2}})}{(x + 1)^{3}} - \frac{(\frac{-2(-1 + 0)}{(-x + 1)^{3}})}{(x + 1)^{2}} - \frac{(\frac{-2(1 + 0)}{(x + 1)^{3}})}{(-x + 1)^{2}}\\=&\frac{24ln(x + 1)}{(-x + 1)^{5}} + \frac{6}{(x + 1)(-x + 1)^{4}} - \frac{6}{(x + 1)^{2}(-x + 1)^{3}} + \frac{18}{(-x + 1)^{4}(x + 1)} + \frac{6}{(x + 1)^{3}(-x + 1)^{2}} - \frac{6}{(-x + 1)^{3}(x + 1)^{2}} - \frac{6}{(x + 1)^{4}(-x + 1)} + \frac{2}{(-x + 1)^{2}(x + 1)^{3}}\\ \end{split}\end{equation} \]

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