There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{\frac{1}{2}}{(1 + {e}^{(x - 4)})} + \frac{\frac{1}{2}}{(1 + {e}^{(x - 20)})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{2}}{({e}^{(x - 4)} + 1)} + \frac{\frac{1}{2}}{({e}^{(x - 20)} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{2}}{({e}^{(x - 4)} + 1)} + \frac{\frac{1}{2}}{({e}^{(x - 20)} + 1)}\right)}{dx}\\=&\frac{1}{2}(\frac{-(({e}^{(x - 4)}((1 + 0)ln(e) + \frac{(x - 4)(0)}{(e)})) + 0)}{({e}^{(x - 4)} + 1)^{2}}) + \frac{1}{2}(\frac{-(({e}^{(x - 20)}((1 + 0)ln(e) + \frac{(x - 20)(0)}{(e)})) + 0)}{({e}^{(x - 20)} + 1)^{2}})\\=&\frac{-{e}^{(x - 4)}}{2({e}^{(x - 4)} + 1)^{2}} - \frac{{e}^{(x - 20)}}{2({e}^{(x - 20)} + 1)^{2}}\\ \end{split}\end{equation} \]

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