There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{142}{(1 + e^{-0.0196875(x - 569.555)})} + 429.752\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{142}{(e^{-0.0196875x + 11.2131140625} + 1)} + 429.752\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{142}{(e^{-0.0196875x + 11.2131140625} + 1)} + 429.752\right)}{dx}\\=&142(\frac{-(e^{-0.0196875x + 11.2131140625}(-0.0196875 + 0) + 0)}{(e^{-0.0196875x + 11.2131140625} + 1)^{2}}) + 0\\=&\frac{2.795625e^{-0.0196875x + 11.2131140625}}{(e^{-0.0196875x + 11.2131140625} + 1)(e^{-0.0196875x + 11.2131140625} + 1)}\\ \end{split}\end{equation} \]

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