There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ e^{2x}*\frac{1}{2}({x}^{2} + x - 2)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{2}e^{2x} + \frac{1}{2}xe^{2x} - e^{2x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{2}e^{2x} + \frac{1}{2}xe^{2x} - e^{2x}\right)}{dx}\\=&\frac{1}{2}*2xe^{2x} + \frac{1}{2}x^{2}e^{2x}*2 + \frac{1}{2}e^{2x} + \frac{1}{2}xe^{2x}*2 - e^{2x}*2\\=&2xe^{2x} + x^{2}e^{2x} - \frac{3e^{2x}}{2}\\ \end{split}\end{equation} \]

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