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

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