There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(e^{3x} - e^{-3x})}{(e^{x} - e^{-x})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{e^{3x}}{(e^{x} - e^{-x})} - \frac{e^{-3x}}{(e^{x} - e^{-x})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{e^{3x}}{(e^{x} - e^{-x})} - \frac{e^{-3x}}{(e^{x} - e^{-x})}\right)}{dx}\\=&(\frac{-(e^{x} - e^{-x}*-1)}{(e^{x} - e^{-x})^{2}})e^{3x} + \frac{e^{3x}*3}{(e^{x} - e^{-x})} - (\frac{-(e^{x} - e^{-x}*-1)}{(e^{x} - e^{-x})^{2}})e^{-3x} - \frac{e^{-3x}*-3}{(e^{x} - e^{-x})}\\=&\frac{-e^{x}e^{3x}}{(e^{x} - e^{-x})^{2}} - \frac{e^{-x}e^{3x}}{(e^{x} - e^{-x})^{2}} + \frac{e^{x}e^{-3x}}{(e^{x} - e^{-x})^{2}} + \frac{e^{-x}e^{-3x}}{(e^{x} - e^{-x})^{2}} + \frac{3e^{3x}}{(e^{x} - e^{-x})} + \frac{3e^{-3x}}{(e^{x} - e^{-x})}\\ \end{split}\end{equation} \]

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