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

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