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

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