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

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