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                                求导函数
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求导函数:
    输入一个原函数(即需要求导的函数),然后设置需要求导的变量和求导的阶数,点击“下一步”按钮,即可获得该函数相应阶数的导函数。
    注意,输入的函数支持数学函数和其它常量。
    当前位置:求导函数 > 导函数计算历史 > 答案
    本次共计算 1 个题目:每一题对 x 求 10 阶导数。
    注意,变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{x}^{({x}^{2} - x)} 关于 x 的 10 阶导数:\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = {x}^{(x^{2} - x)}\\\\ &\color{blue}{函数的 10 阶导数:} \\=&5134752{x}^{(x^{2} - x)}ln^{5}(x) + 14274120x^{2}{x}^{(x^{2} - x)}ln^{6}(x) - 5049660x{x}^{(x^{2} - x)}ln^{6}(x) + 42708456x^{2}{x}^{(x^{2} - x)}ln^{5}(x) - 20844936x{x}^{(x^{2} - x)}ln^{5}(x) + 17612070{x}^{(x^{2} - x)}ln^{4}(x) + 859740{x}^{(x^{2} - x)}ln^{6}(x) + 8341200x^{4}{x}^{(x^{2} - x)}ln^{7}(x) - 5989320x^{3}{x}^{(x^{2} - x)}ln^{7}(x) - \frac{2247420{x}^{(x^{2} - x)}ln^{4}(x)}{x} + 24366930x^{4}{x}^{(x^{2} - x)}ln^{6}(x) - 23423400x^{3}{x}^{(x^{2} - x)}ln^{6}(x) + 2684160x^{2}{x}^{(x^{2} - x)}ln^{7}(x) - \frac{13560{x}^{(x^{2} - x)}ln^{3}(x)}{x^{2}} + 34309920{x}^{(x^{2} - x)}ln^{3}(x) - \frac{7203840{x}^{(x^{2} - x)}ln^{3}(x)}{x} + \frac{603360{x}^{(x^{2} - x)}ln^{2}(x)}{x^{2}} + 41879880x^{4}{x}^{(x^{2} - x)}ln^{5}(x) - 52355520x^{3}{x}^{(x^{2} - x)}ln^{5}(x) + 74636940x^{2}{x}^{(x^{2} - x)}ln^{4}(x) - 49623840x{x}^{(x^{2} - x)}ln^{4}(x) + 1548000x^{6}{x}^{(x^{2} - x)}ln^{8}(x) - 685200x{x}^{(x^{2} - x)}ln^{7}(x) - 1895040x^{5}{x}^{(x^{2} - x)}ln^{8}(x) + 4680000x^{6}{x}^{(x^{2} - x)}ln^{7}(x) - 7621920x^{5}{x}^{(x^{2} - x)}ln^{7}(x) + 44143680x^{4}{x}^{(x^{2} - x)}ln^{4}(x) - 69523230x^{3}{x}^{(x^{2} - x)}ln^{4}(x) + 76795080x^{2}{x}^{(x^{2} - x)}ln^{3}(x) - 68031480x{x}^{(x^{2} - x)}ln^{3}(x) + 36532260{x}^{(x^{2} - x)}ln^{2}(x) + 1537200x^{4}{x}^{(x^{2} - x)}ln^{8}(x) - \frac{12107340{x}^{(x^{2} - x)}ln^{2}(x)}{x} + 8251320x^{6}{x}^{(x^{2} - x)}ln^{6}(x) - 16980600x^{5}{x}^{(x^{2} - x)}ln^{6}(x) + \frac{1354060{x}^{(x^{2} - x)}ln(x)}{x^{2}} + 80520{x}^{(x^{2} - x)}ln^{7}(x) - 807120x^{3}{x}^{(x^{2} - x)}ln^{8}(x) - \frac{376740{x}^{(x^{2} - x)}ln^{5}(x)}{x} - \frac{60480{x}^{(x^{2} - x)}ln^{4}(x)}{x^{2}} + 92160x^{8}{x}^{(x^{2} - x)}ln^{9}(x) - \frac{960{x}^{(x^{2} - x)}ln^{3}(x)}{x^{3}} + \frac{88740{x}^{(x^{2} - x)}ln^{2}(x)}{x^{3}} - 192000x^{7}{x}^{(x^{2} - x)}ln^{9}(x) + \frac{184450{x}^{(x^{2} - x)}ln(x)}{x^{3}} + 9114840x^{6}{x}^{(x^{2} - x)}ln^{5}(x) - 22771476x^{5}{x}^{(x^{2} - x)}ln^{5}(x) + 311040x^{8}{x}^{(x^{2} - x)}ln^{8}(x) + 263565x^{2}{x}^{(x^{2} - x)}ln^{8}(x) + \frac{13365{x}^{(x^{2} - x)}ln^{2}(x)}{x^{4}} - 852480x^{7}{x}^{(x^{2} - x)}ln^{8}(x) + \frac{48540{x}^{(x^{2} - x)}ln(x)}{x^{4}} + 19376080{x}^{(x^{2} - x)}ln(x) - \frac{9687240{x}^{(x^{2} - x)}ln(x)}{x} + 255360x^{6}{x}^{(x^{2} - x)}ln^{9}(x) + 45353430x^{2}{x}^{(x^{2} - x)}ln^{2}(x) + 587520x^{8}{x}^{(x^{2} - x)}ln^{7}(x) - 1960320x^{7}{x}^{(x^{2} - x)}ln^{7}(x) + 28784280x^{4}{x}^{(x^{2} - x)}ln^{3}(x) - 55419120x^{3}{x}^{(x^{2} - x)}ln^{3}(x) + 6508530x^{6}{x}^{(x^{2} - x)}ln^{4}(x) - 52004700x{x}^{(x^{2} - x)}ln^{2}(x) - 19153260x^{5}{x}^{(x^{2} - x)}ln^{4}(x) - 221760x^{5}{x}^{(x^{2} - x)}ln^{9}(x) + 14128080x^{2}{x}^{(x^{2} - x)}ln(x) + 1024x^{10}{x}^{(x^{2} - x)}ln^{10}(x) - 5120x^{9}{x}^{(x^{2} - x)}ln^{10}(x) - 49050x{x}^{(x^{2} - x)}ln^{8}(x) + 5120x^{10}{x}^{(x^{2} - x)}ln^{9}(x) + 695520x^{8}{x}^{(x^{2} - x)}ln^{6}(x) - 2708160x^{7}{x}^{(x^{2} - x)}ln^{6}(x) + 11303460x^{4}{x}^{(x^{2} - x)}ln^{2}(x) - 25919640x^{3}{x}^{(x^{2} - x)}ln^{2}(x) - 20331200x{x}^{(x^{2} - x)}ln(x) + 3007200x^{6}{x}^{(x^{2} - x)}ln^{3}(x) - 10189200x^{5}{x}^{(x^{2} - x)}ln^{3}(x) - 28160x^{9}{x}^{(x^{2} - x)}ln^{9}(x) + 127680x^{4}{x}^{(x^{2} - x)}ln^{9}(x) + 4140{x}^{(x^{2} - x)}ln^{8}(x) + 11520x^{8}{x}^{(x^{2} - x)}ln^{10}(x) - \frac{20370{x}^{(x^{2} - x)}ln^{4}(x)}{x^{3}} + 11520x^{10}{x}^{(x^{2} - x)}ln^{8}(x) - 69120x^{9}{x}^{(x^{2} - x)}ln^{8}(x) - \frac{20160{x}^{(x^{2} - x)}ln^{5}(x)}{x^{2}} - \frac{36120{x}^{(x^{2} - x)}ln^{6}(x)}{x} - 15360x^{7}{x}^{(x^{2} - x)}ln^{10}(x) + 544320x^{8}{x}^{(x^{2} - x)}ln^{5}(x) - 2409120x^{7}{x}^{(x^{2} - x)}ln^{5}(x) - \frac{21480{x}^{(x^{2} - x)}ln^{3}(x)}{x^{4}} + 15360x^{10}{x}^{(x^{2} - x)}ln^{7}(x) - \frac{10260{x}^{(x^{2} - x)}ln^{2}(x)}{x^{5}} + \frac{16880{x}^{(x^{2} - x)}ln(x)}{x^{5}} - 48480x^{3}{x}^{(x^{2} - x)}ln^{9}(x) - 99840x^{9}{x}^{(x^{2} - x)}ln^{7}(x) + \frac{12680{x}^{(x^{2} - x)}ln(x)}{x^{6}} + 13440x^{6}{x}^{(x^{2} - x)}ln^{10}(x) + 13440x^{10}{x}^{(x^{2} - x)}ln^{6}(x) + 2447760x^{4}{x}^{(x^{2} - x)}ln(x) - 94080x^{9}{x}^{(x^{2} - x)}ln^{6}(x) + 287280x^{8}{x}^{(x^{2} - x)}ln^{4}(x) - 1419600x^{7}{x}^{(x^{2} - x)}ln^{4}(x) - 6541380x^{3}{x}^{(x^{2} - x)}ln(x) + \frac{8400{x}^{(x^{2} - x)}ln^{4}(x)}{x^{4}} + 11700x^{2}{x}^{(x^{2} - x)}ln^{9}(x) - \frac{630{x}^{(x^{2} - x)}ln^{6}(x)}{x^{2}} - 8064x^{5}{x}^{(x^{2} - x)}ln^{10}(x) + 8064x^{10}{x}^{(x^{2} - x)}ln^{5}(x) + 869400x^{6}{x}^{(x^{2} - x)}ln^{2}(x) - 3332700x^{5}{x}^{(x^{2} - x)}ln^{2}(x) + \frac{1512{x}^{(x^{2} - x)}ln^{5}(x)}{x^{3}} + \frac{40860{x}^{(x^{2} - x)}ln^{2}(x)}{x^{6}} - \frac{1440{x}^{(x^{2} - x)}ln^{7}(x)}{x} - 60480x^{9}{x}^{(x^{2} - x)}ln^{5}(x) + 3360x^{4}{x}^{(x^{2} - x)}ln^{10}(x) + 101520x^{8}{x}^{(x^{2} - x)}ln^{3}(x) + \frac{23520{x}^{(x^{2} - x)}ln^{3}(x)}{x^{5}} - 552840x^{7}{x}^{(x^{2} - x)}ln^{3}(x) + 3360x^{10}{x}^{(x^{2} - x)}ln^{4}(x) + \frac{35280{x}^{(x^{2} - x)}ln(x)}{x^{7}} + 143160x^{6}{x}^{(x^{2} - x)}ln(x) - 26880x^{9}{x}^{(x^{2} - x)}ln^{4}(x) + 100{x}^{(x^{2} - x)}ln^{9}(x) - 1630x{x}^{(x^{2} - x)}ln^{9}(x) + 23085x^{8}{x}^{(x^{2} - x)}ln^{2}(x) - \frac{50400{x}^{(x^{2} - x)}ln(x)}{x^{8}} - 960x^{3}{x}^{(x^{2} - x)}ln^{10}(x) - \frac{32400{x}^{(x^{2} - x)}ln^{2}(x)}{x^{7}} - 137160x^{7}{x}^{(x^{2} - x)}ln^{2}(x) - 612360x^{5}{x}^{(x^{2} - x)}ln(x) + 960x^{10}{x}^{(x^{2} - x)}ln^{3}(x) - \frac{14400{x}^{(x^{2} - x)}ln^{3}(x)}{x^{6}} - \frac{5040{x}^{(x^{2} - x)}ln^{4}(x)}{x^{5}} - 8160x^{9}{x}^{(x^{2} - x)}ln^{3}(x) + 3060x^{8}{x}^{(x^{2} - x)}ln(x) - \frac{1512{x}^{(x^{2} - x)}ln^{5}(x)}{x^{4}} + 180x^{2}{x}^{(x^{2} - x)}ln^{10}(x) - \frac{420{x}^{(x^{2} - x)}ln^{6}(x)}{x^{3}} - 19680x^{7}{x}^{(x^{2} - x)}ln(x) + 180x^{10}{x}^{(x^{2} - x)}ln^{2}(x) - \frac{120{x}^{(x^{2} - x)}ln^{7}(x)}{x^{2}} - 1620x^{9}{x}^{(x^{2} - x)}ln^{2}(x) - \frac{45{x}^{(x^{2} - x)}ln^{8}(x)}{x} - 20x{x}^{(x^{2} - x)}ln^{10}(x) + 20x^{10}{x}^{(x^{2} - x)}ln(x) - 190x^{9}{x}^{(x^{2} - x)}ln(x) + \frac{12056{x}^{(x^{2} - x)}}{x^{6}} + 10260x^{6}{x}^{(x^{2} - x)} + \frac{21168{x}^{(x^{2} - x)}}{x^{4}} + \frac{73462{x}^{(x^{2} - x)}}{x^{3}} - 48432x^{5}{x}^{(x^{2} - x)} + \frac{14215{x}^{(x^{2} - x)}}{x^{5}} + \frac{10668{x}^{(x^{2} - x)}}{x^{7}} + \frac{796325{x}^{(x^{2} - x)}}{x^{2}} + 1791828x^{2}{x}^{(x^{2} - x)} + \frac{936{x}^{(x^{2} - x)}}{x^{8}} + {x}^{(x^{2} - x)}ln^{10}(x) - \frac{2817540{x}^{(x^{2} - x)}}{x} + 224490x^{4}{x}^{(x^{2} - x)} - 686820x^{3}{x}^{(x^{2} - x)} + 180x^{8}{x}^{(x^{2} - x)} - 1245x^{7}{x}^{(x^{2} - x)} + 3941356{x}^{(x^{2} - x)} - 3144538x{x}^{(x^{2} - x)} - \frac{40320{x}^{(x^{2} - x)}}{x^{9}} + x^{10}{x}^{(x^{2} - x)} - 10x^{9}{x}^{(x^{2} - x)}\\ \end{split}\end{equation} \]



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