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

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