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

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