本次共计算 1 个题目：每一题对 n 求 6 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt({n}^{2} - 7n + 20) - sqrt(n - 4 + \frac{14}{n})sqrt(n - 3) 关于 n 的 6 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - sqrt(n + \frac{14}{n} - 4)sqrt(n - 3) + sqrt(n^{2} - 7n + 20)\\\\ &\color{blue}{函数的 6 阶导数：} \\=& - \frac{47647845sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{11}{2}}n^{10}} + \frac{34034175sqrt(n - 3)}{4(n + \frac{14}{n} - 4)^{\frac{11}{2}}n^{8}} + \frac{15126300sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{9}{2}}n^{9}} - \frac{3781575}{2(n + \frac{14}{n} - 4)^{\frac{9}{2}}(n - 3)^{\frac{1}{2}}n^{8}} - \frac{1620675sqrt(n - 3)}{2(n + \frac{14}{n} - 4)^{\frac{11}{2}}n^{6}} - \frac{1620675sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{9}{2}}n^{7}} + \frac{540225}{2(n + \frac{14}{n} - 4)^{\frac{9}{2}}(n - 3)^{\frac{1}{2}}n^{6}} - \frac{1852200sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{8}} + \frac{308700}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{1}{2}}n^{7}} + \frac{25725}{2(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{6}} + \frac{694575sqrt(n - 3)}{16(n + \frac{14}{n} - 4)^{\frac{11}{2}}n^{4}} + \frac{77175sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{9}{2}}n^{5}} - \frac{77175}{4(n + \frac{14}{n} - 4)^{\frac{9}{2}}(n - 3)^{\frac{1}{2}}n^{4}} + \frac{99225sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{6}} - \frac{22050}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{1}{2}}n^{5}} + \frac{25725}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{3}{2}}n^{6}} - \frac{11025}{8(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{4}} - \frac{19845sqrt(n - 3)}{16(n + \frac{14}{n} - 4)^{\frac{11}{2}}n^{2}} - \frac{11025sqrt(n - 3)}{8(n + \frac{14}{n} - 4)^{\frac{9}{2}}n^{3}} + \frac{105840sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{7}} - \frac{26460}{(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{1}{2}}n^{6}} - \frac{3528}{(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{5}} - \frac{1575sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{4}} - \frac{6615}{8(n - 3)^{\frac{5}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{4}} - \frac{180075}{2(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{3}{2}}n^{8}} - \frac{11025}{4(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{3}{2}}n^{4}} + \frac{111178305sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{11}{2}}n^{12}} - \frac{52942050sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{9}{2}}n^{11}} + \frac{11025}{16(n + \frac{14}{n} - 4)^{\frac{9}{2}}(n - 3)^{\frac{1}{2}}n^{2}} - \frac{1890sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{5}} + \frac{525}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{1}{2}}n^{3}} + \frac{525}{8(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{2}} + \frac{10804500sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{10}} - \frac{1234800sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{9}} + \frac{1323}{2(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{1}{2}}n^{4}} + \frac{15435}{4(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{5}{2}}n^{6}} - \frac{3087}{(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{3}{2}}n^{5}} + \frac{126}{(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{3}} + \frac{88200sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{8}} - \frac{2520sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{6}} + \frac{5294205}{(n + \frac{14}{n} - 4)^{\frac{9}{2}}(n - 3)^{\frac{1}{2}}n^{10}} + \frac{15435}{4(n - 3)^{\frac{5}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{6}} + \frac{24696}{(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{7}} + \frac{945}{16(n - 3)^{\frac{5}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{2}} - \frac{6615}{8(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{5}{2}}n^{4}} - \frac{1440600}{(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{1}{2}}n^{9}} + \frac{441}{4(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{3}{2}}n^{3}} - \frac{11025}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{5}} + \frac{154350}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{7}} + \frac{672}{(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{1}{2}}n^{5}} + \frac{168}{(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{4}} + \frac{588}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{5}} - \frac{3675}{16(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{7}{2}}n^{4}} + \frac{21609}{(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{3}{2}}n^{7}} - \frac{1617}{2(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{5}{2}}n^{5}} - \frac{3675}{8(n - 3)^{\frac{7}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{4}} - \frac{2793}{2(n - 3)^{\frac{5}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{5}} + \frac{399}{4(n - 3)^{\frac{5}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{3}} + \frac{240786}{(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{1}{2}}n^{8}} + \frac{147}{(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{3}{2}}n^{4}} + \frac{525}{2(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{3}} - \frac{180075}{4(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{8}} - \frac{720300}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}n^{9}} - \frac{13230}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{6}} - \frac{17640}{(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{1}{2}}n^{7}} + \frac{525}{8(n - 3)^{\frac{7}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{2}} + \frac{231}{4(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{5}{2}}n^{3}} - \frac{2940}{(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{3}{2}}n^{6}} + \frac{129654}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{8}} + \frac{945sqrt(n - 3)}{64(n + \frac{14}{n} - 4)^{\frac{11}{2}}} + \frac{2205}{16(n - 3)^{\frac{9}{2}}(n + \frac{14}{n} - 4)^{\frac{1}{2}}n^{2}} + \frac{525}{16(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{7}{2}}n^{2}} + \frac{525}{8(n + \frac{14}{n} - 4)^{\frac{1}{2}}(n - 3)^{\frac{7}{2}}n^{3}} + \frac{525}{4(n - 3)^{\frac{7}{2}}(n + \frac{14}{n} - 4)^{\frac{1}{2}}n^{3}} - \frac{3675}{(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{6}} + \frac{441}{2(n - 3)^{\frac{5}{2}}(n + \frac{14}{n} - 4)^{\frac{1}{2}}n^{4}} - \frac{17640}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}n^{7}} + \frac{189}{2(n + \frac{14}{n} - 4)^{\frac{1}{2}}(n - 3)^{\frac{5}{2}}n^{4}} + \frac{945}{16(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{5}{2}}n^{2}} + \frac{525}{4(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{3}{2}}n^{2}} + \frac{294}{(n + \frac{14}{n} - 4)^{\frac{1}{2}}(n - 3)^{\frac{3}{2}}n^{5}} + \frac{336}{(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{1}{2}}n^{5}} + \frac{1260}{(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{1}{2}}n^{6}} + \frac{1260}{(n + \frac{14}{n} - 4)^{\frac{1}{2}}(n - 3)^{\frac{1}{2}}n^{6}} + \frac{567}{2(n - 3)^{\frac{1}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}n^{4}} - \frac{5040sqrt(n - 3)}{(n + \frac{14}{n} - 4)^{\frac{1}{2}}n^{7}} - \frac{315}{32(n + \frac{14}{n} - 4)^{\frac{9}{2}}(n - 3)^{\frac{1}{2}}} - \frac{75}{64(n - 3)^{\frac{3}{2}}(n + \frac{14}{n} - 4)^{\frac{7}{2}}} - \frac{45}{32(n - 3)^{\frac{5}{2}}(n + \frac{14}{n} - 4)^{\frac{5}{2}}} - \frac{75}{32(n - 3)^{\frac{7}{2}}(n + \frac{14}{n} - 4)^{\frac{3}{2}}} + \frac{945sqrt(n + \frac{14}{n} - 4)}{64(n - 3)^{\frac{11}{2}}} - \frac{315}{32(n - 3)^{\frac{9}{2}}(n + \frac{14}{n} - 4)^{\frac{1}{2}}} - \frac{75}{32(n + \frac{14}{n} - 4)^{\frac{7}{2}}(n - 3)^{\frac{3}{2}}} - \frac{75}{64(n + \frac{14}{n} - 4)^{\frac{3}{2}}(n - 3)^{\frac{7}{2}}} - \frac{45}{32(n + \frac{14}{n} - 4)^{\frac{5}{2}}(n - 3)^{\frac{5}{2}}} - \frac{945n^{6}}{(n^{2} - 7n + 20)^{\frac{11}{2}}} + \frac{19845n^{5}}{(n^{2} - 7n + 20)^{\frac{11}{2}}} + \frac{1575n^{4}}{(n^{2} - 7n + 20)^{\frac{9}{2}}} - \frac{694575n^{4}}{4(n^{2} - 7n + 20)^{\frac{11}{2}}} - \frac{22050n^{3}}{(n^{2} - 7n + 20)^{\frac{9}{2}}} + \frac{1620675n^{3}}{2(n^{2} - 7n + 20)^{\frac{11}{2}}} - \frac{675n^{2}}{(n^{2} - 7n + 20)^{\frac{7}{2}}} + \frac{231525n^{2}}{2(n^{2} - 7n + 20)^{\frac{9}{2}}} - \frac{34034175n^{2}}{16(n^{2} - 7n + 20)^{\frac{11}{2}}} + \frac{4725n}{(n^{2} - 7n + 20)^{\frac{7}{2}}} - \frac{540225n}{2(n^{2} - 7n + 20)^{\frac{9}{2}}} + \frac{47647845n}{16(n^{2} - 7n + 20)^{\frac{11}{2}}} - \frac{33075}{4(n^{2} - 7n + 20)^{\frac{7}{2}}} + \frac{45}{(n^{2} - 7n + 20)^{\frac{5}{2}}} + \frac{3781575}{16(n^{2} - 7n + 20)^{\frac{9}{2}}} - \frac{111178305}{64(n^{2} - 7n + 20)^{\frac{11}{2}}}\\ \end{split}\end{equation} \]

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