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

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