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

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