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

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