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

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