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

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