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

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