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

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