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

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