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

Your problem has not been solved here? Please take a look at the  hot problems ！