There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{1}{2}xe^{\frac{-1}{2}x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}xe^{\frac{-1}{2}x}\right)}{dx}\\=&\frac{1}{2}e^{\frac{-1}{2}x} + \frac{1}{2}xe^{\frac{-1}{2}x}*\frac{-1}{2}\\=&\frac{e^{\frac{-1}{2}x}}{2} - \frac{xe^{\frac{-1}{2}x}}{4}\\ \end{split}\end{equation} \]

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