本次共计算 1 个题目：每一题对 x 求 8 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{{x}^{x}}^{x} 关于 x 的 8 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 8 阶导数：} \\=&48{{x}^{x}}^{x}ln^{6}({x}^{x})ln(x) + 96x{{x}^{x}}^{x}ln^{2}(x)ln^{5}({x}^{x}) + 1680x{{x}^{x}}^{x}ln^{3}(x)ln^{3}({x}^{x}) + 280{{x}^{x}}^{x}ln^{2}(x)ln^{4}({x}^{x}) + 2016{{x}^{x}}^{x}ln^{3}(x)ln^{2}({x}^{x}) + \frac{1050{{x}^{x}}^{x}ln(x)ln^{3}({x}^{x})}{x} + 240x{{x}^{x}}^{x}ln^{5}({x}^{x})ln^{2}(x) + 360x^{2}{{x}^{x}}^{x}ln^{3}(x)ln^{4}({x}^{x}) + 3360x^{2}{{x}^{x}}^{x}ln^{4}(x)ln^{2}({x}^{x}) + 928{{x}^{x}}^{x}ln(x)ln^{4}({x}^{x}) + 5376x{{x}^{x}}^{x}ln^{4}(x)ln({x}^{x}) + 1680x{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{3}(x) + 11850{{x}^{x}}^{x}ln^{2}(x)ln^{2}({x}^{x}) + \frac{3528{{x}^{x}}^{x}ln^{2}(x)ln({x}^{x})}{x} + 560{{x}^{x}}^{x}ln^{4}({x}^{x})ln^{2}(x) + 6268x{{x}^{x}}^{x}ln^{2}(x)ln^{3}({x}^{x}) + 9150{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{2}(x) + 1344{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{3}(x) + 31350x{{x}^{x}}^{x}ln^{3}(x)ln({x}^{x}) - \frac{576{{x}^{x}}^{x}ln(x)ln^{2}({x}^{x})}{x^{2}} + 2152{{x}^{x}}^{x}ln^{4}({x}^{x})ln(x) + 18568{{x}^{x}}^{x}ln^{2}({x}^{x})ln(x) + \frac{630{{x}^{x}}^{x}ln^{3}({x}^{x})ln(x)}{x} + 640x^{3}{{x}^{x}}^{x}ln^{4}(x)ln^{3}({x}^{x}) + 2800x^{3}{{x}^{x}}^{x}ln^{5}(x)ln({x}^{x}) + 600x^{4}{{x}^{x}}^{x}ln^{5}(x)ln^{2}({x}^{x}) + 480x^{2}{{x}^{x}}^{x}ln^{4}({x}^{x})ln^{3}(x) + 16042x^{3}{{x}^{x}}^{x}ln^{4}(x)ln({x}^{x}) + 15672x^{2}{{x}^{x}}^{x}ln^{3}(x)ln^{2}({x}^{x}) + \frac{12232{{x}^{x}}^{x}ln(x)ln({x}^{x})}{x} + 1680x^{2}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{4}(x) + 63552x{{x}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 19232{{x}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + 288x^{5}{{x}^{x}}^{x}ln^{6}(x)ln({x}^{x}) + 35x^{5}{{x}^{x}}^{x}ln^{5}(x)ln^{3}({x}^{x}) + 8{{x}^{x}}^{x}ln(x)ln^{6}({x}^{x}) + \frac{456{{x}^{x}}^{x}ln(x)ln({x}^{x})}{x^{3}} + 480x^{3}{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{4}(x) + 3045x^{4}{{x}^{x}}^{x}ln^{4}(x)ln^{2}({x}^{x}) - \frac{432{{x}^{x}}^{x}ln^{2}({x}^{x})ln(x)}{x^{2}} + 10648x^{2}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{3}(x) + 25710x^{2}{{x}^{x}}^{x}ln^{2}(x)ln^{2}({x}^{x}) + 1015x^{2}{{x}^{x}}^{x}ln^{2}(x)ln^{4}({x}^{x}) + 35450x^{3}{{x}^{x}}^{x}ln^{3}(x)ln({x}^{x}) + 8292x{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{2}(x) + 2520x^{3}{{x}^{x}}^{x}ln^{3}(x)ln^{3}({x}^{x}) + 1792x^{5}{{x}^{x}}^{x}ln^{5}(x)ln({x}^{x}) + 35x^{4}{{x}^{x}}^{x}ln^{4}(x)ln^{4}({x}^{x}) + 4560x^{5}{{x}^{x}}^{x}ln^{4}(x)ln({x}^{x}) + 33888x{{x}^{x}}^{x}ln({x}^{x})ln^{2}(x) + 6950x{{x}^{x}}^{x}ln(x)ln^{3}({x}^{x}) + 12930x{{x}^{x}}^{x}ln^{3}({x}^{x})ln(x) + 672x{{x}^{x}}^{x}ln^{5}({x}^{x})ln(x) + 40044x{{x}^{x}}^{x}ln({x}^{x})ln(x) + 240x^{4}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{5}(x) + 21x^{6}{{x}^{x}}^{x}ln^{6}(x)ln^{2}({x}^{x}) + 5952x^{4}{{x}^{x}}^{x}ln^{3}(x)ln^{2}({x}^{x}) + 35x^{4}{{x}^{x}}^{x}ln^{4}({x}^{x})ln^{4}(x) + 6020x^{5}{{x}^{x}}^{x}ln^{3}(x)ln({x}^{x}) + 2520x^{3}{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{3}(x) + 7x^{7}{{x}^{x}}^{x}ln^{7}(x)ln({x}^{x}) + 37344x^{3}{{x}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 48x^{7}{{x}^{x}}^{x}ln^{6}(x)ln({x}^{x}) + 3456x^{3}{{x}^{x}}^{x}ln^{2}(x)ln^{3}({x}^{x}) + 5460x^{4}{{x}^{x}}^{x}ln^{2}(x)ln^{2}({x}^{x}) + 140x^{7}{{x}^{x}}^{x}ln^{5}(x)ln({x}^{x}) + 4256x^{5}{{x}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 21x^{3}{{x}^{x}}^{x}ln^{3}(x)ln^{5}({x}^{x}) + 1925x^{2}{{x}^{x}}^{x}ln^{4}({x}^{x})ln^{2}(x) + 120x^{6}{{x}^{x}}^{x}ln^{5}(x)ln^{2}({x}^{x}) + 160x^{5}{{x}^{x}}^{x}ln^{4}(x)ln^{3}({x}^{x}) + \frac{3112{{x}^{x}}^{x}ln({x}^{x})ln(x)}{x} + 224x^{7}{{x}^{x}}^{x}ln^{4}(x)ln({x}^{x}) + 35x^{3}{{x}^{x}}^{x}ln^{5}({x}^{x})ln^{3}(x) + 392x^{5}{{x}^{x}}^{x}ln({x}^{x})ln^{5}(x) + 53196x{{x}^{x}}^{x}ln(x)ln({x}^{x}) + 280x^{6}{{x}^{x}}^{x}ln^{4}(x)ln^{2}({x}^{x}) + 1575x^{4}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{4}(x) + 120x^{4}{{x}^{x}}^{x}ln^{3}(x)ln^{4}({x}^{x}) + 280x^{5}{{x}^{x}}^{x}ln^{3}(x)ln^{3}({x}^{x}) + 210x^{7}{{x}^{x}}^{x}ln^{3}(x)ln({x}^{x}) + 22296x^{3}{{x}^{x}}^{x}ln({x}^{x})ln^{2}(x) + 21x^{5}{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{5}(x) + 336x^{6}{{x}^{x}}^{x}ln^{3}(x)ln^{2}({x}^{x}) + 17144x^{2}{{x}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + 4128x^{4}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{3}(x) + 1320x^{5}{{x}^{x}}^{x}ln({x}^{x})ln^{4}(x) + 11770x{{x}^{x}}^{x}ln({x}^{x})ln^{3}(x) + 24270x^{2}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{2}(x) + 7x^{2}{{x}^{x}}^{x}ln^{2}(x)ln^{6}({x}^{x}) + 140x^{4}{{x}^{x}}^{x}ln^{2}(x)ln^{4}({x}^{x}) + 18172x^{3}{{x}^{x}}^{x}ln(x)ln({x}^{x}) + 4944x^{3}{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{2}(x) + 2380x^{5}{{x}^{x}}^{x}ln({x}^{x})ln^{3}(x) + 224x^{5}{{x}^{x}}^{x}ln^{2}(x)ln^{3}({x}^{x}) + 48x^{3}{{x}^{x}}^{x}ln^{2}(x)ln^{5}({x}^{x}) + 4678x^{3}{{x}^{x}}^{x}ln({x}^{x})ln^{4}(x) + 7x^{6}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{6}(x) + 112x^{7}{{x}^{x}}^{x}ln^{2}(x)ln({x}^{x}) + 5460x^{4}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{2}(x) + 168x{{x}^{x}}^{x}ln(x)ln^{5}({x}^{x}) + 14670x^{3}{{x}^{x}}^{x}ln({x}^{x})ln^{3}(x) + 210x^{6}{{x}^{x}}^{x}ln^{2}(x)ln^{2}({x}^{x}) + 48x^{6}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{5}(x) + 2464x^{5}{{x}^{x}}^{x}ln({x}^{x})ln^{2}(x) + 140x^{6}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{4}(x) + 24016x^{2}{{x}^{x}}^{x}ln^{2}({x}^{x})ln(x) + 16828x^{3}{{x}^{x}}^{x}ln({x}^{x})ln(x) + 21x^{2}{{x}^{x}}^{x}ln^{6}({x}^{x})ln^{2}(x) + 120x^{5}{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{4}(x) + 816x^{2}{{x}^{x}}^{x}ln(x)ln^{4}({x}^{x}) + 160x^{4}{{x}^{x}}^{x}ln^{4}({x}^{x})ln^{3}(x) + 4340x^{3}{{x}^{x}}^{x}ln^{3}({x}^{x})ln(x) + 224x^{6}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{3}(x) + 3696x^{4}{{x}^{x}}^{x}ln^{2}({x}^{x})ln(x) + 280x^{5}{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{3}(x) + 1820x^{3}{{x}^{x}}^{x}ln(x)ln^{3}({x}^{x}) + 2544x^{2}{{x}^{x}}^{x}ln^{4}({x}^{x})ln(x) + 1428x^{5}{{x}^{x}}^{x}ln(x)ln({x}^{x}) + 120x^{3}{{x}^{x}}^{x}ln^{5}({x}^{x})ln^{2}(x) + 2184x^{4}{{x}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + 1680{{x}^{x}}^{x}ln^{4}(x) + 1428x^{5}{{x}^{x}}^{x}ln({x}^{x})ln(x) + 280x^{4}{{x}^{x}}^{x}ln^{4}({x}^{x})ln^{2}(x) + 210x^{6}{{x}^{x}}^{x}ln^{2}({x}^{x})ln^{2}(x) + 336x^{5}{{x}^{x}}^{x}ln^{3}({x}^{x})ln^{2}(x) + 48x^{2}{{x}^{x}}^{x}ln^{6}({x}^{x})ln(x) + 224x^{4}{{x}^{x}}^{x}ln^{4}({x}^{x})ln(x) + 1344x{{x}^{x}}^{x}ln({x}^{x})ln^{4}(x) + 20580{{x}^{x}}^{x}ln^{2}({x}^{x}) + 7x{{x}^{x}}^{x}ln^{7}({x}^{x})ln(x) + x{{x}^{x}}^{x}ln(x)ln^{7}({x}^{x}) + 70x^{5}{{x}^{x}}^{x}ln(x)ln^{3}({x}^{x}) + 84{{x}^{x}}^{x}ln^{6}({x}^{x}) + 140x^{3}{{x}^{x}}^{x}ln^{5}({x}^{x})ln(x) + 2450{{x}^{x}}^{x}ln^{4}({x}^{x}) + 560x^{3}{{x}^{x}}^{x}ln({x}^{x})ln^{5}(x) + 28x^{7}{{x}^{x}}^{x}ln(x)ln({x}^{x}) + 56x^{4}{{x}^{x}}^{x}ln(x)ln^{4}({x}^{x}) + 112x^{6}{{x}^{x}}^{x}ln^{2}({x}^{x})ln(x) + \frac{216{{x}^{x}}^{x}ln({x}^{x})ln(x)}{x^{3}} + 56x^{6}{{x}^{x}}^{x}ln(x)ln^{2}({x}^{x}) + 8x^{2}{{x}^{x}}^{x}ln(x)ln^{6}({x}^{x}) + 210x^{5}{{x}^{x}}^{x}ln^{3}({x}^{x})ln(x) + 54152{{x}^{x}}^{x}ln(x) + 28x^{7}{{x}^{x}}^{x}ln({x}^{x})ln(x) + 56x^{7}{{x}^{x}}^{x}ln({x}^{x})ln^{2}(x) + 48x^{5}{{x}^{x}}^{x}ln({x}^{x})ln^{6}(x) + 70x^{7}{{x}^{x}}^{x}ln({x}^{x})ln^{3}(x) + 28x^{7}{{x}^{x}}^{x}ln({x}^{x})ln^{5}(x) + \frac{504{{x}^{x}}^{x}ln({x}^{x})ln^{2}(x)}{x} + 56x^{7}{{x}^{x}}^{x}ln({x}^{x})ln^{4}(x) + 28x^{3}{{x}^{x}}^{x}ln(x)ln^{5}({x}^{x}) + x^{7}{{x}^{x}}^{x}ln({x}^{x})ln^{7}(x) + 8x^{7}{{x}^{x}}^{x}ln({x}^{x})ln^{6}(x) + 2520x^{6}{{x}^{x}}^{x}ln^{3}(x) + 3360x^{2}{{x}^{x}}^{x}ln^{5}(x) + 5992x^{4}{{x}^{x}}^{x}ln^{5}(x) + 15344{{x}^{x}}^{x}ln^{3}(x) + 56x^{6}{{x}^{x}}^{x}ln^{7}(x) + 65800x^{2}{{x}^{x}}^{x}ln^{3}(x) + 1260x^{2}{{x}^{x}}^{x}ln^{4}({x}^{x}) + 23940x^{2}{{x}^{x}}^{x}ln^{4}(x) + \frac{12992{{x}^{x}}^{x}ln({x}^{x})}{x} + 840x^{4}{{x}^{x}}^{x}ln^{6}(x) + 1596x^{6}{{x}^{x}}^{x}ln^{2}(x) + 12460x^{2}{{x}^{x}}^{x}ln^{2}({x}^{x}) + 87780x^{2}{{x}^{x}}^{x}ln^{2}(x) + 23380x^{4}{{x}^{x}}^{x}ln^{2}(x) + 1680x^{3}{{x}^{x}}^{x}ln^{3}({x}^{x}) + 560x^{6}{{x}^{x}}^{x}ln(x) + 27160x^{4}{{x}^{x}}^{x}ln^{3}(x) + \frac{2800{{x}^{x}}^{x}ln^{3}({x}^{x})}{x} + 420x^{6}{{x}^{x}}^{x}ln^{6}(x) + 17570x^{4}{{x}^{x}}^{x}ln^{4}(x) + 504x{{x}^{x}}^{x}ln^{5}({x}^{x}) + 8680x{{x}^{x}}^{x}ln^{3}({x}^{x}) + 2380x^{6}{{x}^{x}}^{x}ln^{4}(x) - \frac{672{{x}^{x}}^{x}ln^{2}(x)}{x^{2}} + 504x^{5}{{x}^{x}}^{x}ln({x}^{x}) - \frac{1232{{x}^{x}}^{x}ln(x)}{x^{2}} + 45472{{x}^{x}}^{x}ln^{2}(x) + 1344x^{6}{{x}^{x}}^{x}ln^{5}(x) + 57120x^{2}{{x}^{x}}^{x}ln(x) - \frac{140{{x}^{x}}^{x}ln^{4}({x}^{x})}{x^{2}} + x^{8}{{x}^{x}}^{x}ln^{8}(x) + 8x^{8}{{x}^{x}}^{x}ln^{7}(x) + 28x^{8}{{x}^{x}}^{x}ln^{6}(x) + 32200x{{x}^{x}}^{x}ln({x}^{x}) + 56x^{8}{{x}^{x}}^{x}ln^{5}(x) + 70x^{8}{{x}^{x}}^{x}ln^{4}(x) + \frac{112{{x}^{x}}^{x}ln^{5}({x}^{x})}{x} + 10640x^{4}{{x}^{x}}^{x}ln(x) + 56x^{8}{{x}^{x}}^{x}ln^{3}(x) + 1260x^{4}{{x}^{x}}^{x}ln^{2}({x}^{x}) + 8120x^{3}{{x}^{x}}^{x}ln({x}^{x}) + 28x^{8}{{x}^{x}}^{x}ln^{2}(x) - \frac{288{{x}^{x}}^{x}ln(x)}{x^{4}} + {{x}^{x}}^{x}ln^{8}({x}^{x}) - \frac{728{{x}^{x}}^{x}ln^{2}({x}^{x})}{x^{2}} + 22449{{x}^{x}}^{x} + 8x{{x}^{x}}^{x}ln^{7}({x}^{x}) + 28x^{2}{{x}^{x}}^{x}ln^{6}({x}^{x}) + \frac{224{{x}^{x}}^{x}ln^{3}({x}^{x})}{x^{3}} + \frac{384{{x}^{x}}^{x}ln({x}^{x})}{x^{5}} - \frac{336{{x}^{x}}^{x}ln^{2}({x}^{x})}{x^{4}} + 56x^{3}{{x}^{x}}^{x}ln^{5}({x}^{x}) + \frac{224{{x}^{x}}^{x}ln({x}^{x})}{x^{3}} + 70x^{4}{{x}^{x}}^{x}ln^{4}({x}^{x}) + 56x^{5}{{x}^{x}}^{x}ln^{3}({x}^{x}) + 28x^{6}{{x}^{x}}^{x}ln^{2}({x}^{x}) + 8x^{7}{{x}^{x}}^{x}ln({x}^{x}) + 8x^{8}{{x}^{x}}^{x}ln(x) + 14560x^{2}{{x}^{x}}^{x} + \frac{140{{x}^{x}}^{x}}{x^{2}} + 84x^{6}{{x}^{x}}^{x} + 2002x^{4}{{x}^{x}}^{x} - \frac{36{{x}^{x}}^{x}}{x^{4}} - \frac{240{{x}^{x}}^{x}}{x^{6}} + x^{8}{{x}^{x}}^{x}\\ \end{split}\end{equation} \]

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