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

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