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

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