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

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