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

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