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 9 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{(1 + {(sin(x))}^{3})}^{\frac{1}{3}} 关于 x 的 9 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (sin^{3}(x) + 1)^{\frac{1}{3}}\\\\ &\color{blue}{函数的 9 阶导数：} \\=&\frac{96342400sin^{18}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{26}{3}}} - \frac{301593600sin^{15}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{23}{3}}} + \frac{150796800sin^{17}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{23}{3}}} + \frac{351859200sin^{12}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} - \frac{439824000sin^{14}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} + \frac{79168320sin^{16}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} - \frac{186278400sin^{9}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{465696000sin^{11}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} - \frac{212667840sin^{13}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{15523200sin^{15}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{42873600sin^{6}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{213628800sin^{8}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} + \frac{200434080sin^{10}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{37699200sin^{12}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} + \frac{831600sin^{14}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{3225600sin^{3}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} + \frac{38707200sin^{5}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{76742400sin^{7}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} + \frac{30609600sin^{9}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{1764000sin^{11}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{1747200sin^{2}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{9996000sin^{4}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{22400cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} - \frac{9130600sin^{6}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{1156050sin^{8}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} - \frac{188160sin(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} + \frac{698640sin^{3}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} - \frac{228570sin^{5}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} - \frac{1640cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{2}{3}}} + \frac{4921sin^{2}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{2}{3}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{(1 + {(sin(x))}^{3})}^{\frac{1}{3}} 关于 x 的 9 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (sin^{3}(x) + 1)^{\frac{1}{3}}\\\\ &\color{blue}{函数的 9 阶导数：} \\=&\frac{96342400sin^{18}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{26}{3}}} - \frac{301593600sin^{15}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{23}{3}}} + \frac{150796800sin^{17}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{23}{3}}} + \frac{351859200sin^{12}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} - \frac{439824000sin^{14}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} + \frac{79168320sin^{16}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{20}{3}}} - \frac{186278400sin^{9}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{465696000sin^{11}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} - \frac{212667840sin^{13}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{15523200sin^{15}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{17}{3}}} + \frac{42873600sin^{6}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{213628800sin^{8}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} + \frac{200434080sin^{10}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{37699200sin^{12}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} + \frac{831600sin^{14}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{14}{3}}} - \frac{3225600sin^{3}(x)cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} + \frac{38707200sin^{5}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{76742400sin^{7}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} + \frac{30609600sin^{9}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{1764000sin^{11}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{11}{3}}} - \frac{1747200sin^{2}(x)cos^{7}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{9996000sin^{4}(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{22400cos^{9}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} - \frac{9130600sin^{6}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} + \frac{1156050sin^{8}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{8}{3}}} - \frac{188160sin(x)cos^{5}(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} + \frac{698640sin^{3}(x)cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} - \frac{228570sin^{5}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{5}{3}}} - \frac{1640cos^{3}(x)}{(sin^{3}(x) + 1)^{\frac{2}{3}}} + \frac{4921sin^{2}(x)cos(x)}{(sin^{3}(x) + 1)^{\frac{2}{3}}}\\ \end{split}\end{equation} \]
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