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

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