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

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