There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{({x}^{3} - 3x)}{(x - arctan(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{3}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{3}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))}\right)}{dx}\\=&(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})x^{3} + \frac{3x^{2}}{(x - arctan(x))} - 3(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})x - \frac{3}{(x - arctan(x))}\\=&\frac{x^{3}}{(x - arctan(x))^{2}(x^{2} + 1)} - \frac{x^{3}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))^{2}(x^{2} + 1)} + \frac{3x}{(x - arctan(x))^{2}} - \frac{3}{(x - arctan(x))}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{x^{3}}{(x - arctan(x))^{2}(x^{2} + 1)} - \frac{x^{3}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))} - \frac{3x}{(x - arctan(x))^{2}(x^{2} + 1)} + \frac{3x}{(x - arctan(x))^{2}} - \frac{3}{(x - arctan(x))}\right)}{dx}\\=&\frac{(\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x^{3}}{(x^{2} + 1)} + \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{3}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))^{2}(x^{2} + 1)} - (\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x^{3} - \frac{3x^{2}}{(x - arctan(x))^{2}} + 3(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})x^{2} + \frac{3*2x}{(x - arctan(x))} - \frac{3(\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x}{(x^{2} + 1)} - \frac{3(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x}{(x - arctan(x))^{2}} - \frac{3}{(x - arctan(x))^{2}(x^{2} + 1)} + 3(\frac{-2(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{3}})x + \frac{3}{(x - arctan(x))^{2}} - 3(\frac{-(1 - (\frac{(1)}{(1 + (x)^{2})}))}{(x - arctan(x))^{2}})\\=&\frac{2x^{3}}{(x - arctan(x))^{3}(x^{2} + 1)^{2}} - \frac{4x^{3}}{(x - arctan(x))^{3}(x^{2} + 1)} - \frac{2x^{4}}{(x - arctan(x))^{2}(x^{2} + 1)^{2}} + \frac{3x^{2}}{(x^{2} + 1)(x - arctan(x))^{2}} + \frac{2x^{3}}{(x - arctan(x))^{3}} - \frac{6x^{2}}{(x - arctan(x))^{2}} + \frac{3x^{2}}{(x - arctan(x))^{2}(x^{2} + 1)} + \frac{6x}{(x - arctan(x))} - \frac{6x}{(x - arctan(x))^{3}(x^{2} + 1)^{2}} + \frac{12x}{(x - arctan(x))^{3}(x^{2} + 1)} + \frac{6x^{2}}{(x - arctan(x))^{2}(x^{2} + 1)^{2}} - \frac{6}{(x - arctan(x))^{2}(x^{2} + 1)} - \frac{6x}{(x - arctan(x))^{3}} + \frac{6}{(x - arctan(x))^{2}}\\ \end{split}\end{equation} \]

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