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

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