本次共计算 1 个题目：每一题对 x 求 15 阶导数。
    注意，变量是区分大小写的。
$$\begin{equation}\begin{split}【1/1】求函数{x}^{x} 关于 x 的 15 阶导数：\\\end{split}\end{equation}$$ $$\begin{equation}\begin{split}\\解:&\\ \\ &\color{blue}{函数的 15 阶导数：} \\=&{x}^{x}ln^{15}(x) + 15{x}^{x}ln^{14}(x) + \frac{105{x}^{x}ln^{13}(x)}{x} + 105{x}^{x}ln^{13}(x) + 455{x}^{x}ln^{12}(x) + \frac{1365{x}^{x}ln^{12}(x)}{x} - \frac{455{x}^{x}ln^{12}(x)}{x^{2}} + 1365{x}^{x}ln^{11}(x) + 3003{x}^{x}ln^{10}(x) + \frac{8190{x}^{x}ln^{11}(x)}{x} + 5005{x}^{x}ln^{9}(x) + 6435{x}^{x}ln^{8}(x) + \frac{30030{x}^{x}ln^{10}(x)}{x} + \frac{15015{x}^{x}ln^{10}(x)}{x^{2}} + \frac{2730{x}^{x}ln^{11}(x)}{x^{3}} + 6435{x}^{x}ln^{7}(x) + 5005{x}^{x}ln^{6}(x) + \frac{75075{x}^{x}ln^{9}(x)}{x} + 3003{x}^{x}ln^{5}(x) + 1365{x}^{x}ln^{4}(x) + \frac{135135{x}^{x}ln^{8}(x)}{x} + \frac{125125{x}^{x}ln^{9}(x)}{x^{2}} + 455{x}^{x}ln^{3}(x) + 105{x}^{x}ln^{2}(x) + \frac{180180{x}^{x}ln^{7}(x)}{x} + \frac{180180{x}^{x}ln^{6}(x)}{x} + \frac{450450{x}^{x}ln^{8}(x)}{x^{2}} - \frac{75075{x}^{x}ln^{9}(x)}{x^{3}} - \frac{225225{x}^{x}ln^{8}(x)}{x^{3}} - \frac{18018{x}^{x}ln^{10}(x)}{x^{4}} + \frac{20020{x}^{x}ln^{9}(x)}{x^{4}} + \frac{135135{x}^{x}ln^{5}(x)}{x} + \frac{75075{x}^{x}ln^{4}(x)}{x} + \frac{990990{x}^{x}ln^{7}(x)}{x^{2}} + \frac{30030{x}^{x}ln^{3}(x)}{x} + \frac{8190{x}^{x}ln^{2}(x)}{x} + \frac{1471470{x}^{x}ln^{6}(x)}{x^{2}} + \frac{1365{x}^{x}ln(x)}{x} + \frac{1531530{x}^{x}ln^{5}(x)}{x^{2}} + \frac{1126125{x}^{x}ln^{4}(x)}{x^{2}} - \frac{1365{x}^{x}ln^{11}(x)}{x^{2}} + \frac{1261260{x}^{x}ln^{6}(x)}{x^{3}} + \frac{315315{x}^{x}ln^{8}(x)}{x^{4}} + \frac{120120{x}^{x}ln^{9}(x)}{x^{5}} - \frac{180180{x}^{x}ln^{8}(x)}{x^{5}} - \frac{1156155{x}^{x}ln^{6}(x)}{x^{4}} - \frac{772200{x}^{x}ln^{8}(x)}{x^{6}} - \frac{1261260{x}^{x}ln^{7}(x)}{x^{5}} + \frac{1209780{x}^{x}ln^{7}(x)}{x^{6}} + \frac{4633200{x}^{x}ln^{7}(x)}{x^{7}} + \frac{315315{x}^{x}ln^{7}(x)}{x^{4}} + \frac{575575{x}^{x}ln^{3}(x)}{x^{2}} + \frac{4724720{x}^{x}ln^{6}(x)}{x^{6}} + \frac{195195{x}^{x}ln^{2}(x)}{x^{2}} - \frac{6846840{x}^{x}ln^{6}(x)}{x^{7}} + \frac{3153150{x}^{x}ln^{5}(x)}{x^{3}} - \frac{25225200{x}^{x}ln^{6}(x)}{x^{8}} + \frac{39585{x}^{x}ln(x)}{x^{2}} - \frac{2963961{x}^{x}ln^{5}(x)}{x^{4}} - \frac{2462460{x}^{x}ln^{5}(x)}{x^{6}} + \frac{4054050{x}^{x}ln^{4}(x)}{x^{3}} - \frac{16036020{x}^{x}ln^{5}(x)}{x^{7}} + \frac{3153150{x}^{x}ln^{3}(x)}{x^{3}} + \frac{4099095{x}^{x}ln^{5}(x)}{x^{5}} + \frac{1501500{x}^{x}ln^{2}(x)}{x^{3}} + \frac{33081048{x}^{x}ln^{5}(x)}{x^{8}} + \frac{121080960{x}^{x}ln^{5}(x)}{x^{9}} - \frac{2207205{x}^{x}ln^{4}(x)}{x^{4}} + \frac{4099095{x}^{x}ln^{4}(x)}{x^{5}} + \frac{12312300{x}^{x}ln^{4}(x)}{x^{7}} + \frac{47387340{x}^{x}ln^{4}(x)}{x^{8}} - \frac{134053920{x}^{x}ln^{4}(x)}{x^{9}} - \frac{10435425{x}^{x}ln^{4}(x)}{x^{6}} - \frac{495331200{x}^{x}ln^{4}(x)}{x^{10}} + \frac{465465{x}^{x}ln^{3}(x)}{x^{4}} - \frac{630630{x}^{x}ln^{3}(x)}{x^{5}} + \frac{20870850{x}^{x}ln^{3}(x)}{x^{7}} - \frac{39659620{x}^{x}ln^{3}(x)}{x^{8}} - \frac{115915800{x}^{x}ln^{3}(x)}{x^{9}} + \frac{438852960{x}^{x}ln^{3}(x)}{x^{10}} + \frac{1651104000{x}^{x}ln^{3}(x)}{x^{11}} - \frac{3478475{x}^{x}ln^{3}(x)}{x^{6}} + \frac{1666665{x}^{x}ln^{2}(x)}{x^{4}} - \frac{2612610{x}^{x}ln^{2}(x)}{x^{5}} + \frac{3708705{x}^{x}ln^{2}(x)}{x^{6}} - \frac{31501470{x}^{x}ln^{2}(x)}{x^{8}} + \frac{90210120{x}^{x}ln^{2}(x)}{x^{9}} + \frac{218279880{x}^{x}ln^{2}(x)}{x^{10}} - \frac{1088942400{x}^{x}ln^{2}(x)}{x^{11}} - \frac{4191264000{x}^{x}ln^{2}(x)}{x^{12}} + \frac{405405{x}^{x}ln(x)}{x^{3}} + \frac{945945{x}^{x}ln(x)}{x^{4}} - \frac{1126125{x}^{x}ln(x)}{x^{5}} + \frac{2125695{x}^{x}ln(x)}{x^{6}} + \frac{4444440{x}^{x}ln(x)}{x^{8}} + \frac{31891860{x}^{x}ln(x)}{x^{9}} - \frac{134479800{x}^{x}ln(x)}{x^{10}} - \frac{279311760{x}^{x}ln(x)}{x^{11}} + \frac{1820059200{x}^{x}ln(x)}{x^{12}} - \frac{4669665{x}^{x}ln(x)}{x^{7}} + \frac{7185024000{x}^{x}ln(x)}{x^{13}} + \frac{47775{x}^{x}}{x^{3}} + \frac{182182{x}^{x}}{x^{4}} - \frac{105105{x}^{x}}{x^{5}} + \frac{168740{x}^{x}}{x^{6}} - \frac{667095{x}^{x}}{x^{7}} - \frac{4444440{x}^{x}}{x^{9}} - \frac{16072420{x}^{x}}{x^{10}} + \frac{100136400{x}^{x}}{x^{11}} + \frac{180973584{x}^{x}}{x^{12}} + \frac{3640{x}^{x}}{x^{2}} - \frac{1535880960{x}^{x}}{x^{13}} + \frac{2475473{x}^{x}}{x^{8}} + 15{x}^{x}ln(x) + \frac{105{x}^{x}}{x} - \frac{6227020800{x}^{x}}{x^{14}} + {x}^{x}\\ \end{split}\end{equation}$$

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