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

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