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

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