There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ -sin(x) + \frac{2{e}^{(-2x)}}{({({e}^{(-2x)} + 1)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -sin(x) + \frac{2{e}^{(-2x)}}{({e}^{(-2x)} + 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -sin(x) + \frac{2{e}^{(-2x)}}{({e}^{(-2x)} + 1)^{2}}\right)}{dx}\\=&-cos(x) + 2(\frac{-2(({e}^{(-2x)}((-2)ln(e) + \frac{(-2x)(0)}{(e)})) + 0)}{({e}^{(-2x)} + 1)^{3}}){e}^{(-2x)} + \frac{2({e}^{(-2x)}((-2)ln(e) + \frac{(-2x)(0)}{(e)}))}{({e}^{(-2x)} + 1)^{2}}\\=&-cos(x) + \frac{8{e}^{(-4x)}}{({e}^{(-2x)} + 1)^{3}} - \frac{4{e}^{(-2x)}}{({e}^{(-2x)} + 1)^{2}}\\ \end{split}\end{equation} \]

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