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

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