There are 1 questions in this calculation: for each question, the 13 derivative of x is calculated.
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\[ \begin{equation}\begin{split}[1/1]Find\ the\ 13th\ derivative\ of\ function\ {x}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 13th\ derivative\ of\ function:} \\=&{x}^{x}ln^{13}(x) + 13{x}^{x}ln^{12}(x) + \frac{78{x}^{x}ln^{11}(x)}{x} + 78{x}^{x}ln^{11}(x) + 286{x}^{x}ln^{10}(x) + \frac{858{x}^{x}ln^{10}(x)}{x} - \frac{286{x}^{x}ln^{10}(x)}{x^{2}} + 715{x}^{x}ln^{9}(x) + 1287{x}^{x}ln^{8}(x) + \frac{4290{x}^{x}ln^{9}(x)}{x} + 1716{x}^{x}ln^{7}(x) + 1716{x}^{x}ln^{6}(x) + \frac{12870{x}^{x}ln^{8}(x)}{x} + \frac{6435{x}^{x}ln^{8}(x)}{x^{2}} + \frac{1430{x}^{x}ln^{9}(x)}{x^{3}} + 1287{x}^{x}ln^{5}(x) + 715{x}^{x}ln^{4}(x) + \frac{25740{x}^{x}ln^{7}(x)}{x} + 286{x}^{x}ln^{3}(x) + 78{x}^{x}ln^{2}(x) + \frac{36036{x}^{x}ln^{6}(x)}{x} + \frac{42900{x}^{x}ln^{7}(x)}{x^{2}} + \frac{36036{x}^{x}ln^{5}(x)}{x} + \frac{25740{x}^{x}ln^{4}(x)}{x} + \frac{120120{x}^{x}ln^{6}(x)}{x^{2}} - \frac{25740{x}^{x}ln^{7}(x)}{x^{3}} - \frac{60060{x}^{x}ln^{6}(x)}{x^{3}} - \frac{7722{x}^{x}ln^{8}(x)}{x^{4}} + \frac{6864{x}^{x}ln^{7}(x)}{x^{4}} + \frac{12870{x}^{x}ln^{3}(x)}{x} + \frac{4290{x}^{x}ln^{2}(x)}{x} + \frac{198198{x}^{x}ln^{5}(x)}{x^{2}} + \frac{858{x}^{x}ln(x)}{x} + \frac{210210{x}^{x}ln^{4}(x)}{x^{2}} - \frac{715{x}^{x}ln^{9}(x)}{x^{2}} + \frac{145860{x}^{x}ln^{3}(x)}{x^{2}} + \frac{41184{x}^{x}ln^{7}(x)}{x^{5}} + \frac{64350{x}^{x}ln^{2}(x)}{x^{2}} - \frac{48048{x}^{x}ln^{6}(x)}{x^{5}} + \frac{180180{x}^{x}ln^{4}(x)}{x^{3}} + \frac{84084{x}^{x}ln^{6}(x)}{x^{4}} - \frac{205920{x}^{x}ln^{6}(x)}{x^{6}} - \frac{252252{x}^{x}ln^{5}(x)}{x^{5}} - \frac{165165{x}^{x}ln^{4}(x)}{x^{4}} + \frac{241956{x}^{x}ln^{5}(x)}{x^{6}} + \frac{926640{x}^{x}ln^{5}(x)}{x^{7}} + \frac{63063{x}^{x}ln^{5}(x)}{x^{4}} + \frac{674960{x}^{x}ln^{4}(x)}{x^{6}} - \frac{978120{x}^{x}ln^{4}(x)}{x^{7}} + \frac{16445{x}^{x}ln(x)}{x^{2}} - \frac{3603600{x}^{x}ln^{4}(x)}{x^{8}} + \frac{300300{x}^{x}ln^{3}(x)}{x^{3}} - \frac{282282{x}^{x}ln^{3}(x)}{x^{4}} - \frac{234520{x}^{x}ln^{3}(x)}{x^{6}} + \frac{231660{x}^{x}ln^{2}(x)}{x^{3}} - \frac{1527240{x}^{x}ln^{3}(x)}{x^{7}} + \frac{390390{x}^{x}ln^{3}(x)}{x^{5}} + \frac{3150576{x}^{x}ln^{3}(x)}{x^{8}} + \frac{11531520{x}^{x}ln^{3}(x)}{x^{9}} - \frac{126126{x}^{x}ln^{2}(x)}{x^{4}} + \frac{90090{x}^{x}ln(x)}{x^{3}} + \frac{234234{x}^{x}ln^{2}(x)}{x^{5}} + \frac{703560{x}^{x}ln^{2}(x)}{x^{7}} + \frac{2707848{x}^{x}ln^{2}(x)}{x^{8}} - \frac{7660224{x}^{x}ln^{2}(x)}{x^{9}} - \frac{596310{x}^{x}ln^{2}(x)}{x^{6}} - \frac{28304640{x}^{x}ln^{2}(x)}{x^{10}} + \frac{13299{x}^{x}ln(x)}{x^{4}} - \frac{18018{x}^{x}ln(x)}{x^{5}} + \frac{596310{x}^{x}ln(x)}{x^{7}} - \frac{1133132{x}^{x}ln(x)}{x^{8}} - \frac{3311880{x}^{x}ln(x)}{x^{9}} + \frac{12538656{x}^{x}ln(x)}{x^{10}} + \frac{47174400{x}^{x}ln(x)}{x^{11}} - \frac{99385{x}^{x}ln(x)}{x^{6}} + \frac{14300{x}^{x}}{x^{3}} - \frac{24882{x}^{x}}{x^{5}} + \frac{35321{x}^{x}}{x^{6}} - \frac{300014{x}^{x}}{x^{8}} + \frac{859144{x}^{x}}{x^{9}} + \frac{2078856{x}^{x}}{x^{10}} + \frac{1859{x}^{x}}{x^{2}} + \frac{15873{x}^{x}}{x^{4}} - \frac{10370880{x}^{x}}{x^{11}} + 13{x}^{x}ln(x) + \frac{78{x}^{x}}{x} - \frac{39916800{x}^{x}}{x^{12}} + {x}^{x}\\ \end{split}\end{equation} \]

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