There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (x - 1)log_{3}^{x} + \frac{e^{3}xlog_{3}^{x}(x - 5)}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{2}log_{3}^{x}e^{3} - log_{3}^{x} - \frac{5}{2}xlog_{3}^{x}e^{3} + xlog_{3}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{2}log_{3}^{x}e^{3} - log_{3}^{x} - \frac{5}{2}xlog_{3}^{x}e^{3} + xlog_{3}^{x}\right)}{dx}\\=&\frac{1}{2}*2xlog_{3}^{x}e^{3} + \frac{1}{2}x^{2}(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))})e^{3} + \frac{1}{2}x^{2}log_{3}^{x}e^{3}*0 - (\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))}) - \frac{5}{2}log_{3}^{x}e^{3} - \frac{5}{2}x(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))})e^{3} - \frac{5}{2}xlog_{3}^{x}e^{3}*0 + log_{3}^{x} + x(\frac{(\frac{(1)}{(x)} - \frac{(0)log_{3}^{x}}{(3)})}{(ln(3))})\\=&xlog_{3}^{x}e^{3} + \frac{xe^{3}}{2ln(3)} - \frac{1}{xln(3)} - \frac{5log_{3}^{x}e^{3}}{2} - \frac{5e^{3}}{2ln(3)} + log_{3}^{x} + \frac{1}{ln(3)}\\ \end{split}\end{equation} \]

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