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。
\[ \begin{equation}\begin{split}【1/1】求函数log_{3{x}^{2}}^{x} 关于 x 的 15 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = log_{3x^{2}}^{x}\\\\ &\color{blue}{函数的 15 阶导数：} \\=&\frac{87178291200}{x^{15}ln(3x^{2})} + \frac{1133862589440}{x^{15}ln^{2}(3x^{2})} + \frac{9411763147776}{x^{15}ln^{3}(3x^{2})} + \frac{59709937996800}{x^{15}ln^{4}(3x^{2})} + \frac{306665482905600}{x^{15}ln^{5}(3x^{2})} + \frac{1305523970150400}{x^{15}ln^{6}(3x^{2})} + \frac{4647871203655680}{x^{15}ln^{7}(3x^{2})} + \frac{13838875674624000}{x^{15}ln^{8}(3x^{2})} + \frac{34224436953907200}{x^{15}ln^{9}(3x^{2})} + \frac{69324177162240000}{x^{15}ln^{10}(3x^{2})} + \frac{112395367474790400}{x^{15}ln^{11}(3x^{2})} + \frac{140601148047360000}{x^{15}ln^{12}(3x^{2})} + \frac{127656915369984000}{x^{15}ln^{13}(3x^{2})} + \frac{74987278958592000}{x^{15}ln^{14}(3x^{2})} + \frac{21424936845312000}{x^{15}ln^{15}(3x^{2})} - \frac{174356582400log_{3x^{2}}^{x}}{x^{15}ln(3x^{2})} - \frac{2267725178880log_{3x^{2}}^{x}}{x^{15}ln^{2}(3x^{2})} - \frac{18823526295552log_{3x^{2}}^{x}}{x^{15}ln^{3}(3x^{2})} - \frac{119419875993600log_{3x^{2}}^{x}}{x^{15}ln^{4}(3x^{2})} - \frac{613330965811200log_{3x^{2}}^{x}}{x^{15}ln^{5}(3x^{2})} - \frac{2611047940300800log_{3x^{2}}^{x}}{x^{15}ln^{6}(3x^{2})} - \frac{9295742407311360log_{3x^{2}}^{x}}{x^{15}ln^{7}(3x^{2})} - \frac{27677751349248000log_{3x^{2}}^{x}}{x^{15}ln^{8}(3x^{2})} - \frac{68448873907814400log_{3x^{2}}^{x}}{x^{15}ln^{9}(3x^{2})} - \frac{138648354324480000log_{3x^{2}}^{x}}{x^{15}ln^{10}(3x^{2})} - \frac{224790734949580800log_{3x^{2}}^{x}}{x^{15}ln^{11}(3x^{2})} - \frac{281202296094720000log_{3x^{2}}^{x}}{x^{15}ln^{12}(3x^{2})} - \frac{255313830739968000log_{3x^{2}}^{x}}{x^{15}ln^{13}(3x^{2})} - \frac{149974557917184000log_{3x^{2}}^{x}}{x^{15}ln^{14}(3x^{2})} - \frac{42849873690624000log_{3x^{2}}^{x}}{x^{15}ln^{15}(3x^{2})}\\ \end{split}\end{equation} \]

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