There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2 + {e}^{\frac{1}{x}})}{(1 + {e}^{(\frac{2}{x})})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{e}^{\frac{1}{x}}}{({e}^{(\frac{2}{x})} + 1)} + \frac{2}{({e}^{(\frac{2}{x})} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{e}^{\frac{1}{x}}}{({e}^{(\frac{2}{x})} + 1)} + \frac{2}{({e}^{(\frac{2}{x})} + 1)}\right)}{dx}\\=&(\frac{-(({e}^{(\frac{2}{x})}((\frac{2*-1}{x^{2}})ln(e) + \frac{(\frac{2}{x})(0)}{(e)})) + 0)}{({e}^{(\frac{2}{x})} + 1)^{2}}){e}^{\frac{1}{x}} + \frac{({e}^{\frac{1}{x}}((\frac{-1}{x^{2}})ln(e) + \frac{(\frac{1}{x})(0)}{(e)}))}{({e}^{(\frac{2}{x})} + 1)} + 2(\frac{-(({e}^{(\frac{2}{x})}((\frac{2*-1}{x^{2}})ln(e) + \frac{(\frac{2}{x})(0)}{(e)})) + 0)}{({e}^{(\frac{2}{x})} + 1)^{2}})\\=&\frac{-{e}^{\frac{1}{x}}}{({e}^{(\frac{2}{x})} + 1)x^{2}} + \frac{2{e}^{(\frac{3}{x})}}{({e}^{(\frac{2}{x})} + 1)^{2}x^{2}} + \frac{4{e}^{(\frac{2}{x})}}{({e}^{(\frac{2}{x})} + 1)^{2}x^{2}}\\ \end{split}\end{equation} \]

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