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

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