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

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