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

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