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

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