There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ arctan(\frac{(x + 1)}{(x - 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = arctan(\frac{x}{(x - 1)} + \frac{1}{(x - 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( arctan(\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}}))}{(1 + (\frac{x}{(x - 1)} + \frac{1}{(x - 1)})^{2})})\\=&\frac{-x}{(x - 1)^{2}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{1}{(x - 1)^{2}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} + \frac{1}{(x - 1)(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-x}{(x - 1)^{2}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{1}{(x - 1)^{2}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} + \frac{1}{(x - 1)(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)}\right)}{dx}\\=&\frac{-(\frac{-2(1 + 0)}{(x - 1)^{3}})x}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{(\frac{-((\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} + \frac{2x}{(x - 1)^{2}} + 2(\frac{-2(1 + 0)}{(x - 1)^{3}})x + \frac{2}{(x - 1)^{2}} + (\frac{-2(1 + 0)}{(x - 1)^{3}}) + 0)}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}})x}{(x - 1)^{2}} - \frac{1}{(x - 1)^{2}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{(\frac{-2(1 + 0)}{(x - 1)^{3}})}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{(\frac{-((\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} + \frac{2x}{(x - 1)^{2}} + 2(\frac{-2(1 + 0)}{(x - 1)^{3}})x + \frac{2}{(x - 1)^{2}} + (\frac{-2(1 + 0)}{(x - 1)^{3}}) + 0)}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}})}{(x - 1)^{2}} + \frac{(\frac{-(1 + 0)}{(x - 1)^{2}})}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} + \frac{(\frac{-((\frac{-2(1 + 0)}{(x - 1)^{3}})x^{2} + \frac{2x}{(x - 1)^{2}} + 2(\frac{-2(1 + 0)}{(x - 1)^{3}})x + \frac{2}{(x - 1)^{2}} + (\frac{-2(1 + 0)}{(x - 1)^{3}}) + 0)}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}})}{(x - 1)}\\=&\frac{2x}{(x - 1)^{3}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{2x^{3}}{(x - 1)^{5}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}} + \frac{2x^{2}}{(x - 1)^{4}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}} - \frac{6x^{2}}{(x - 1)^{5}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}} + \frac{4x}{(x - 1)^{4}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}} - \frac{6x}{(x - 1)^{5}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}} + \frac{2x^{2}}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}(x - 1)^{4}} + \frac{4x}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}(x - 1)^{4}} - \frac{2x}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}(x - 1)^{3}} + \frac{2}{(x - 1)^{3}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{2}{(x - 1)^{2}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)} - \frac{2}{(x - 1)^{5}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}} + \frac{2}{(x - 1)^{4}(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}} + \frac{2}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}(x - 1)^{4}} - \frac{2}{(\frac{x^{2}}{(x - 1)^{2}} + \frac{2x}{(x - 1)^{2}} + \frac{1}{(x - 1)^{2}} + 1)^{2}(x - 1)^{3}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！