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

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