There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ x - arctan(x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x - arctan(x)\right)}{dx}\\=&1 - (\frac{(1)}{(1 + (x)^{2})})\\=& - \frac{1}{(x^{2} + 1)} + 1\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( - \frac{1}{(x^{2} + 1)} + 1\right)}{dx}\\=& - (\frac{-(2x + 0)}{(x^{2} + 1)^{2}}) + 0\\=&\frac{2x}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2x}{(x^{2} + 1)^{2}}\right)}{dx}\\=&2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x + \frac{2}{(x^{2} + 1)^{2}}\\=& - \frac{8x^{2}}{(x^{2} + 1)^{3}} + \frac{2}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( - \frac{8x^{2}}{(x^{2} + 1)^{3}} + \frac{2}{(x^{2} + 1)^{2}}\right)}{dx}\\=& - 8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2} - \frac{8*2x}{(x^{2} + 1)^{3}} + 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})\\=&\frac{48x^{3}}{(x^{2} + 1)^{4}} - \frac{24x}{(x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

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