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

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