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

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