There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}\right)}{dx}\\=&({{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}((1)ln({{{{x}^{x}}^{x}}^{x}}^{x}) + \frac{(x)(({{{{x}^{x}}^{x}}^{x}}^{x}((1)ln({{{x}^{x}}^{x}}^{x}) + \frac{(x)(({{{x}^{x}}^{x}}^{x}((1)ln({{x}^{x}}^{x}) + \frac{(x)(({{x}^{x}}^{x}((1)ln({x}^{x}) + \frac{(x)(({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))}{({x}^{x})})))}{({{x}^{x}}^{x})})))}{({{{x}^{x}}^{x}}^{x})})))}{({{{{x}^{x}}^{x}}^{x}}^{x})}))\\=&{{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}ln({{{{x}^{x}}^{x}}^{x}}^{x}) + x{{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}ln({{{x}^{x}}^{x}}^{x}) + x^{2}{{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}ln({{x}^{x}}^{x}) + x^{3}{{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}ln({x}^{x}) + x^{4}{{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}ln(x) + x^{4}{{{{{x}^{x}}^{x}}^{x}}^{x}}^{x}\\ \end{split}\end{equation} \]

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