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

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