There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ ln(\frac{(2 - {x}^{2})}{(1 - {x}^{2})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})\right)}{dx}\\=&\frac{(-(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x^{2} - \frac{2x}{(-x^{2} + 1)} + 2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}}))}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})}\\=&\frac{-2x^{3}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{2}} - \frac{2x}{(-x^{2} + 1)(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})} + \frac{4x}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2x^{3}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{2}} - \frac{2x}{(-x^{2} + 1)(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})} + \frac{4x}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{2}}\right)}{dx}\\=&\frac{-2(\frac{-(-(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x^{2} - \frac{2x}{(-x^{2} + 1)} + 2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}}))}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}})x^{3}}{(-x^{2} + 1)^{2}} - \frac{2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x^{3}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})} - \frac{2*3x^{2}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{2}} - \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})} - \frac{2(\frac{-(-(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x^{2} - \frac{2x}{(-x^{2} + 1)} + 2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}}))}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}})x}{(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})} + \frac{4(\frac{-(-(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x^{2} - \frac{2x}{(-x^{2} + 1)} + 2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}}))}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}})x}{(-x^{2} + 1)^{2}} + \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})} + \frac{4}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{2}}\\=&\frac{-4x^{6}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}(-x^{2} + 1)^{4}} - \frac{8x^{4}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}(-x^{2} + 1)^{3}} + \frac{16x^{4}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}(-x^{2} + 1)^{4}} - \frac{8x^{4}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{3}} - \frac{10x^{2}}{(-x^{2} + 1)^{2}(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})} - \frac{4x^{2}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}(-x^{2} + 1)^{2}} + \frac{16x^{2}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}(-x^{2} + 1)^{3}} + \frac{16x^{2}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{3}} - \frac{16x^{2}}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})^{2}(-x^{2} + 1)^{4}} + \frac{4}{(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})(-x^{2} + 1)^{2}} - \frac{2}{(-x^{2} + 1)(\frac{-x^{2}}{(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)})}\\ \end{split}\end{equation} \]

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