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

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