There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ \frac{-1}{(1 + {x}^{2})(-{\frac{1}{x}}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{(x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{(x^{2} + 1)}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x^{2} + \frac{2x}{(x^{2} + 1)}\\=&\frac{-2x^{3}}{(x^{2} + 1)^{2}} + \frac{2x}{(x^{2} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x^{3}}{(x^{2} + 1)^{2}} + \frac{2x}{(x^{2} + 1)}\right)}{dx}\\=&-2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{3} - \frac{2*3x^{2}}{(x^{2} + 1)^{2}} + 2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x + \frac{2}{(x^{2} + 1)}\\=&\frac{8x^{4}}{(x^{2} + 1)^{3}} - \frac{10x^{2}}{(x^{2} + 1)^{2}} + \frac{2}{(x^{2} + 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{8x^{4}}{(x^{2} + 1)^{3}} - \frac{10x^{2}}{(x^{2} + 1)^{2}} + \frac{2}{(x^{2} + 1)}\right)}{dx}\\=&8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{4} + \frac{8*4x^{3}}{(x^{2} + 1)^{3}} - 10(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{10*2x}{(x^{2} + 1)^{2}} + 2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})\\=&\frac{-48x^{5}}{(x^{2} + 1)^{4}} + \frac{72x^{3}}{(x^{2} + 1)^{3}} - \frac{24x}{(x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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