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。
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。
本次共计算 1 个题目：每一题对 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数8sqrt(5{x}^{9} + 2{x}^{10}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 8sqrt(5x^{9} + 2x^{10})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 8sqrt(5x^{9} + 2x^{10})\right)}{dx}\\=&\frac{8(5*9x^{8} + 2*10x^{9})*\frac{1}{2}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\=&\frac{180x^{8}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} + \frac{80x^{9}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{180x^{8}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} + \frac{80x^{9}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\right)}{dx}\\=&180(\frac{\frac{-1}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{3}{2}}})x^{8} + \frac{180*8x^{7}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} + 80(\frac{\frac{-1}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{3}{2}}})x^{9} + \frac{80*9x^{8}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\=&\frac{-4050x^{16}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} - \frac{3600x^{17}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{1440x^{7}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} - \frac{800x^{18}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{720x^{8}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-4050x^{16}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} - \frac{3600x^{17}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{1440x^{7}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} - \frac{800x^{18}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{720x^{8}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\right)}{dx}\\=&-4050(\frac{\frac{-3}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{5}{2}}})x^{16} - \frac{4050*16x^{15}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} - 3600(\frac{\frac{-3}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{5}{2}}})x^{17} - \frac{3600*17x^{16}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + 1440(\frac{\frac{-1}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{3}{2}}})x^{7} + \frac{1440*7x^{6}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} - 800(\frac{\frac{-3}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{5}{2}}})x^{18} - \frac{800*18x^{17}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + 720(\frac{\frac{-1}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{3}{2}}})x^{8} + \frac{720*8x^{7}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\=&\frac{273375x^{24}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} + \frac{364500x^{25}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{97200x^{15}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{162000x^{26}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{91800x^{16}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{10080x^{6}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} + \frac{24000x^{27}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{21600x^{17}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{5760x^{7}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{273375x^{24}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} + \frac{364500x^{25}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{97200x^{15}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{162000x^{26}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{91800x^{16}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{10080x^{6}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} + \frac{24000x^{27}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{21600x^{17}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{5760x^{7}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\right)}{dx}\\=&273375(\frac{\frac{-5}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{7}{2}}})x^{24} + \frac{273375*24x^{23}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} + 364500(\frac{\frac{-5}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{7}{2}}})x^{25} + \frac{364500*25x^{24}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - 97200(\frac{\frac{-3}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{5}{2}}})x^{15} - \frac{97200*15x^{14}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + 162000(\frac{\frac{-5}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{7}{2}}})x^{26} + \frac{162000*26x^{25}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - 91800(\frac{\frac{-3}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{5}{2}}})x^{16} - \frac{91800*16x^{15}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + 10080(\frac{\frac{-1}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{3}{2}}})x^{6} + \frac{10080*6x^{5}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} + 24000(\frac{\frac{-5}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{7}{2}}})x^{27} + \frac{24000*27x^{26}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - 21600(\frac{\frac{-3}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{5}{2}}})x^{17} - \frac{21600*17x^{16}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + 5760(\frac{\frac{-1}{2}(5*9x^{8} + 2*10x^{9})}{(5x^{9} + 2x^{10})^{\frac{3}{2}}})x^{7} + \frac{5760*7x^{6}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\=&\frac{-61509375x^{32}}{2(5x^{9} + 2x^{10})^{\frac{7}{2}}} - \frac{54675000x^{33}}{(5x^{9} + 2x^{10})^{\frac{7}{2}}} + \frac{13122000x^{23}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{36450000x^{34}}{(5x^{9} + 2x^{10})^{\frac{7}{2}}} + \frac{18225000x^{24}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{1684800x^{14}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} - \frac{10800000x^{35}}{(5x^{9} + 2x^{10})^{\frac{7}{2}}} + \frac{8424000x^{25}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{1699200x^{15}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{60480x^{5}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}} - \frac{1200000x^{36}}{(5x^{9} + 2x^{10})^{\frac{7}{2}}} + \frac{1296000x^{26}}{(5x^{9} + 2x^{10})^{\frac{5}{2}}} - \frac{424800x^{16}}{(5x^{9} + 2x^{10})^{\frac{3}{2}}} + \frac{40320x^{6}}{(5x^{9} + 2x^{10})^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
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