There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ 36(\frac{1}{x} - \frac{1}{(e^{x} - 1)})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{36}{x} - \frac{36}{(e^{x} - 1)}\right)}{dx}\\=&\frac{36*-1}{x^{2}} - 36(\frac{-(e^{x} + 0)}{(e^{x} - 1)^{2}})\\=&\frac{-36}{x^{2}} + \frac{36e^{x}}{(e^{x} - 1)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-36}{x^{2}} + \frac{36e^{x}}{(e^{x} - 1)^{2}}\right)}{dx}\\=&\frac{-36*-2}{x^{3}} + 36(\frac{-2(e^{x} + 0)}{(e^{x} - 1)^{3}})e^{x} + \frac{36e^{x}}{(e^{x} - 1)^{2}}\\=&\frac{72}{x^{3}} - \frac{72e^{{x}*{2}}}{(e^{x} - 1)^{3}} + \frac{36e^{x}}{(e^{x} - 1)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{72}{x^{3}} - \frac{72e^{{x}*{2}}}{(e^{x} - 1)^{3}} + \frac{36e^{x}}{(e^{x} - 1)^{2}}\right)}{dx}\\=&\frac{72*-3}{x^{4}} - 72(\frac{-3(e^{x} + 0)}{(e^{x} - 1)^{4}})e^{{x}*{2}} - \frac{72*2e^{x}e^{x}}{(e^{x} - 1)^{3}} + 36(\frac{-2(e^{x} + 0)}{(e^{x} - 1)^{3}})e^{x} + \frac{36e^{x}}{(e^{x} - 1)^{2}}\\=&\frac{-216}{x^{4}} + \frac{216e^{{x}*{3}}}{(e^{x} - 1)^{4}} - \frac{216e^{{x}*{2}}}{(e^{x} - 1)^{3}} + \frac{36e^{x}}{(e^{x} - 1)^{2}}\\ \end{split}\end{equation} \]

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