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

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