There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(x(3{(e^{x})}^{2} - 2e^{x} + 3))}{(3{(e^{x} - 1)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{xe^{{x}*{2}}}{(e^{x} - 1)^{2}} - \frac{\frac{2}{3}xe^{x}}{(e^{x} - 1)^{2}} + \frac{x}{(e^{x} - 1)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{xe^{{x}*{2}}}{(e^{x} - 1)^{2}} - \frac{\frac{2}{3}xe^{x}}{(e^{x} - 1)^{2}} + \frac{x}{(e^{x} - 1)^{2}}\right)}{dx}\\=&(\frac{-2(e^{x} + 0)}{(e^{x} - 1)^{3}})xe^{{x}*{2}} + \frac{e^{{x}*{2}}}{(e^{x} - 1)^{2}} + \frac{x*2e^{x}e^{x}}{(e^{x} - 1)^{2}} - \frac{2}{3}(\frac{-2(e^{x} + 0)}{(e^{x} - 1)^{3}})xe^{x} - \frac{\frac{2}{3}e^{x}}{(e^{x} - 1)^{2}} - \frac{\frac{2}{3}xe^{x}}{(e^{x} - 1)^{2}} + (\frac{-2(e^{x} + 0)}{(e^{x} - 1)^{3}})x + \frac{1}{(e^{x} - 1)^{2}}\\=&\frac{-2xe^{{x}*{3}}}{(e^{x} - 1)^{3}} + \frac{e^{{x}*{2}}}{(e^{x} - 1)^{2}} + \frac{2xe^{{x}*{2}}}{(e^{x} - 1)^{2}} + \frac{4xe^{{x}*{2}}}{3(e^{x} - 1)^{3}} - \frac{2e^{x}}{3(e^{x} - 1)^{2}} - \frac{2xe^{x}}{3(e^{x} - 1)^{2}} - \frac{2xe^{x}}{(e^{x} - 1)^{3}} + \frac{1}{(e^{x} - 1)^{2}}\\ \end{split}\end{equation} \]

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