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

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