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

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