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

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