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

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