There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{2}{e}^{\frac{1}{2}}x\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3}e^{\frac{1}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3}e^{\frac{1}{2}}\right)}{dx}\\=&3x^{2}e^{\frac{1}{2}} + \frac{x^{3}*\frac{1}{2}*0}{e^{\frac{1}{2}}}\\=&3x^{2}e^{\frac{1}{2}}\\ \end{split}\end{equation} \]

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