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

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