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

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