There are 1 questions in this calculation: for each question, the 15 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 15th\ derivative\ of\ function\ {{e}^{x}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 15th\ derivative\ of\ function:} \\=&{{e}^{x}}^{x}ln^{15}({e}^{x}) + 15x{{e}^{x}}^{x}ln^{14}({e}^{x}) + 210{{e}^{x}}^{x}ln^{13}({e}^{x}) + 105x^{2}{{e}^{x}}^{x}ln^{13}({e}^{x}) + 2730x{{e}^{x}}^{x}ln^{12}({e}^{x}) + 16380{{e}^{x}}^{x}ln^{11}({e}^{x}) + 455x^{3}{{e}^{x}}^{x}ln^{12}({e}^{x}) + 16380x^{2}{{e}^{x}}^{x}ln^{11}({e}^{x}) + 180180x{{e}^{x}}^{x}ln^{10}({e}^{x}) + 600600{{e}^{x}}^{x}ln^{9}({e}^{x}) + 1365x^{4}{{e}^{x}}^{x}ln^{11}({e}^{x}) + 60060x^{3}{{e}^{x}}^{x}ln^{10}({e}^{x}) + 900900x^{2}{{e}^{x}}^{x}ln^{9}({e}^{x}) + 5405400x{{e}^{x}}^{x}ln^{8}({e}^{x}) + 10810800{{e}^{x}}^{x}ln^{7}({e}^{x}) + 3003x^{5}{{e}^{x}}^{x}ln^{10}({e}^{x}) + 150150x^{4}{{e}^{x}}^{x}ln^{9}({e}^{x}) + 2702700x^{3}{{e}^{x}}^{x}ln^{8}({e}^{x}) + 21621600x^{2}{{e}^{x}}^{x}ln^{7}({e}^{x}) + 75675600x{{e}^{x}}^{x}ln^{6}({e}^{x}) + 90810720{{e}^{x}}^{x}ln^{5}({e}^{x}) + 5005x^{6}{{e}^{x}}^{x}ln^{9}({e}^{x}) + 270270x^{5}{{e}^{x}}^{x}ln^{8}({e}^{x}) + 5405400x^{4}{{e}^{x}}^{x}ln^{7}({e}^{x}) + 50450400x^{3}{{e}^{x}}^{x}ln^{6}({e}^{x}) + 227026800x^{2}{{e}^{x}}^{x}ln^{5}({e}^{x}) + 454053600x{{e}^{x}}^{x}ln^{4}({e}^{x}) + 302702400{{e}^{x}}^{x}ln^{3}({e}^{x}) + 6435x^{7}{{e}^{x}}^{x}ln^{8}({e}^{x}) + 360360x^{6}{{e}^{x}}^{x}ln^{7}({e}^{x}) + 7567560x^{5}{{e}^{x}}^{x}ln^{6}({e}^{x}) + 75675600x^{4}{{e}^{x}}^{x}ln^{5}({e}^{x}) + 378378000x^{3}{{e}^{x}}^{x}ln^{4}({e}^{x}) + 908107200x^{2}{{e}^{x}}^{x}ln^{3}({e}^{x}) + 908107200x{{e}^{x}}^{x}ln^{2}({e}^{x}) + 259459200{{e}^{x}}^{x}ln({e}^{x}) + 6435x^{8}{{e}^{x}}^{x}ln^{7}({e}^{x}) + 360360x^{7}{{e}^{x}}^{x}ln^{6}({e}^{x}) + 7567560x^{6}{{e}^{x}}^{x}ln^{5}({e}^{x}) + 75675600x^{5}{{e}^{x}}^{x}ln^{4}({e}^{x}) + 378378000x^{4}{{e}^{x}}^{x}ln^{3}({e}^{x}) + 908107200x^{3}{{e}^{x}}^{x}ln^{2}({e}^{x}) + 908107200x^{2}{{e}^{x}}^{x}ln({e}^{x}) + 270270x^{8}{{e}^{x}}^{x}ln^{5}({e}^{x}) + 5005x^{9}{{e}^{x}}^{x}ln^{6}({e}^{x}) + 5405400x^{7}{{e}^{x}}^{x}ln^{4}({e}^{x}) + 50450400x^{6}{{e}^{x}}^{x}ln^{3}({e}^{x}) + 227026800x^{5}{{e}^{x}}^{x}ln^{2}({e}^{x}) + 454053600x^{4}{{e}^{x}}^{x}ln({e}^{x}) + 21621600x^{7}{{e}^{x}}^{x}ln^{2}({e}^{x}) + 2702700x^{8}{{e}^{x}}^{x}ln^{3}({e}^{x}) + 150150x^{9}{{e}^{x}}^{x}ln^{4}({e}^{x}) + 75675600x^{6}{{e}^{x}}^{x}ln({e}^{x}) + 3003x^{10}{{e}^{x}}^{x}ln^{5}({e}^{x}) + 5405400x^{8}{{e}^{x}}^{x}ln({e}^{x}) + 900900x^{9}{{e}^{x}}^{x}ln^{2}({e}^{x}) + 180180x^{10}{{e}^{x}}^{x}ln({e}^{x}) + 60060x^{10}{{e}^{x}}^{x}ln^{3}({e}^{x}) + 16380x^{11}{{e}^{x}}^{x}ln^{2}({e}^{x}) + 2730x^{12}{{e}^{x}}^{x}ln({e}^{x}) + 1365x^{11}{{e}^{x}}^{x}ln^{4}({e}^{x}) + 455x^{12}{{e}^{x}}^{x}ln^{3}({e}^{x}) + 105x^{13}{{e}^{x}}^{x}ln^{2}({e}^{x}) + 15x^{14}{{e}^{x}}^{x}ln({e}^{x}) + 259459200x{{e}^{x}}^{x} + 10810800x^{7}{{e}^{x}}^{x} + 90810720x^{5}{{e}^{x}}^{x} + 600600x^{9}{{e}^{x}}^{x} + 302702400x^{3}{{e}^{x}}^{x} + 16380x^{11}{{e}^{x}}^{x} + 210x^{13}{{e}^{x}}^{x} + x^{15}{{e}^{x}}^{x}\\ \end{split}\end{equation} \]

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