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

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