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

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