There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{\frac{8}{5}}{(1 + {e}^{(-15x)})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{8}{5}}{({e}^{(-15x)} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{8}{5}}{({e}^{(-15x)} + 1)}\right)}{dx}\\=&\frac{8}{5}(\frac{-(({e}^{(-15x)}((-15)ln(e) + \frac{(-15x)(0)}{(e)})) + 0)}{({e}^{(-15x)} + 1)^{2}})\\=&\frac{24{e}^{(-15x)}}{({e}^{(-15x)} + 1)^{2}}\\ \end{split}\end{equation} \]

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