There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(\frac{(1 + e^{x - 5})}{(1 + e^{-x - 5})})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(\frac{e^{x - 5}}{(e^{-x - 5} + 1)} + \frac{1}{(e^{-x - 5} + 1)})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(\frac{e^{x - 5}}{(e^{-x - 5} + 1)} + \frac{1}{(e^{-x - 5} + 1)})\right)}{dx}\\=&\frac{((\frac{-(e^{-x - 5}(-1 + 0) + 0)}{(e^{-x - 5} + 1)^{2}})e^{x - 5} + \frac{e^{x - 5}(1 + 0)}{(e^{-x - 5} + 1)} + (\frac{-(e^{-x - 5}(-1 + 0) + 0)}{(e^{-x - 5} + 1)^{2}}))}{(\frac{e^{x - 5}}{(e^{-x - 5} + 1)} + \frac{1}{(e^{-x - 5} + 1)})}\\=&\frac{e^{-x - 5}e^{x - 5}}{(\frac{e^{x - 5}}{(e^{-x - 5} + 1)} + \frac{1}{(e^{-x - 5} + 1)})(e^{-x - 5} + 1)^{2}} + \frac{e^{x - 5}}{(e^{-x - 5} + 1)(\frac{e^{x - 5}}{(e^{-x - 5} + 1)} + \frac{1}{(e^{-x - 5} + 1)})} + \frac{e^{-x - 5}}{(\frac{e^{x - 5}}{(e^{-x - 5} + 1)} + \frac{1}{(e^{-x - 5} + 1)})(e^{-x - 5} + 1)^{2}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！