There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ (1 - {x}^{2}){\frac{1}{((1 + {x}^{2}))}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - \frac{x^{2}}{(x^{2} + 1)^{2}} + \frac{1}{(x^{2} + 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - \frac{x^{2}}{(x^{2} + 1)^{2}} + \frac{1}{(x^{2} + 1)^{2}}\right)}{dx}\\=& - (\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{2x}{(x^{2} + 1)^{2}} + (\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})\\=&\frac{4x^{3}}{(x^{2} + 1)^{3}} - \frac{2x}{(x^{2} + 1)^{2}} - \frac{4x}{(x^{2} + 1)^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{4x^{3}}{(x^{2} + 1)^{3}} - \frac{2x}{(x^{2} + 1)^{2}} - \frac{4x}{(x^{2} + 1)^{3}}\right)}{dx}\\=&4(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{3} + \frac{4*3x^{2}}{(x^{2} + 1)^{3}} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x - \frac{2}{(x^{2} + 1)^{2}} - 4(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x - \frac{4}{(x^{2} + 1)^{3}}\\=& - \frac{24x^{4}}{(x^{2} + 1)^{4}} + \frac{20x^{2}}{(x^{2} + 1)^{3}} + \frac{24x^{2}}{(x^{2} + 1)^{4}} - \frac{4}{(x^{2} + 1)^{3}} - \frac{2}{(x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]

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