There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}\right)}{dx}\\=&({x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}((({x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}((({x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}((({x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}((({x}^{{x}^{{x}^{{x}^{x}}}}((({x}^{{x}^{{x}^{x}}}((({x}^{{x}^{x}}((({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})))ln(x) + \frac{({x}^{x})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{x}})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{{x}^{x}}})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{{x}^{{x}^{x}}}})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{{x}^{{x}^{{x}^{x}}}}})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}})(1)}{(x)})))ln(x) + \frac{({x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}})(1)}{(x)}))\\=&{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}{x}^{{x}^{{x}^{{x}^{x}}}}{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln^{8}(x) + {x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}{x}^{{x}^{{x}^{{x}^{x}}}}{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln^{7}(x) + \frac{{x}^{x}{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}{x}^{{x}^{{x}^{{x}^{x}}}}{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln^{6}(x)}{x} + \frac{{x}^{{x}^{x}}{x}^{{x}^{{x}^{x}}}{x}^{{x}^{{x}^{{x}^{x}}}}{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln^{5}(x)}{x} + \frac{{x}^{{x}^{{x}^{x}}}{x}^{{x}^{{x}^{{x}^{x}}}}{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln^{4}(x)}{x} + \frac{{x}^{{x}^{{x}^{{x}^{x}}}}{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln^{3}(x)}{x} + \frac{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln^{2}(x)}{x} + \frac{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}ln(x)}{x} + \frac{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{{x}^{x}}}}}}}}}{x}\\ \end{split}\end{equation} \]

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