There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{122.23}{(12.8192 + e^{x - 57.74})} - 0.449\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{122.23}{(e^{x - 57.74} + 12.8192)} - 0.449\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{122.23}{(e^{x - 57.74} + 12.8192)} - 0.449\right)}{dx}\\=&122.23(\frac{-(e^{x - 57.74}(1 + 0) + 0)}{(e^{x - 57.74} + 12.8192)^{2}}) + 0\\=&\frac{-122.23e^{x - 57.74}}{(e^{x - 57.74} + 12.8192)(e^{x - 57.74} + 12.8192)}\\ \end{split}\end{equation} \]

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