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

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