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。
\[ \begin{equation}\begin{split}【1/1】求函数th(th(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( th(th(x))\right)}{dx}\\=&(1 - th^{2}(th(x)))(1 - th^{2}(x))\\=&th^{2}(x)th^{2}(th(x)) - th^{2}(th(x)) - th^{2}(x) + 1\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( th^{2}(x)th^{2}(th(x)) - th^{2}(th(x)) - th^{2}(x) + 1\right)}{dx}\\=&2th(x)(1 - th^{2}(x))th^{2}(th(x)) + th^{2}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2th(x)(1 - th^{2}(x)) + 0\\=&2th(x)th^{2}(th(x)) - 2th^{3}(x)th^{2}(th(x)) + 2th(th(x))th^{2}(x) - 2th^{4}(x)th(th(x)) - 4th^{3}(th(x))th^{2}(x) + 2th^{4}(x)th^{3}(th(x)) + 2th^{2}(x)th(th(x)) - 2th(th(x)) + 2th^{3}(th(x)) - 2th(x) + 2th^{3}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2th(x)th^{2}(th(x)) - 2th^{3}(x)th^{2}(th(x)) + 2th(th(x))th^{2}(x) - 2th^{4}(x)th(th(x)) - 4th^{3}(th(x))th^{2}(x) + 2th^{4}(x)th^{3}(th(x)) + 2th^{2}(x)th(th(x)) - 2th(th(x)) + 2th^{3}(th(x)) - 2th(x) + 2th^{3}(x)\right)}{dx}\\=&2(1 - th^{2}(x))th^{2}(th(x)) + 2th(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2*3th^{2}(x)(1 - th^{2}(x))th^{2}(th(x)) - 2th^{3}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 2(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) + 2th(th(x))*2th(x)(1 - th^{2}(x)) - 2*4th^{3}(x)(1 - th^{2}(x))th(th(x)) - 2th^{4}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 4*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) - 4th^{3}(th(x))*2th(x)(1 - th^{2}(x)) + 2*4th^{3}(x)(1 - th^{2}(x))th^{3}(th(x)) + 2th^{4}(x)*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 2*2th(x)(1 - th^{2}(x))th(th(x)) + 2th^{2}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 2*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2(1 - th^{2}(x)) + 2*3th^{2}(x)(1 - th^{2}(x))\\=& - 18th^{2}(x)th^{2}(th(x)) + 22th^{4}(x)th^{2}(th(x)) + 8th(th(x))th(x) - 20th^{3}(x)th(th(x)) - 12th^{3}(th(x))th(x) + 20th^{3}(x)th^{3}(th(x)) - 4th(th(x))th^{3}(x) + 12th^{5}(x)th(th(x)) + 4th^{3}(th(x))th^{3}(x) - 12th^{5}(x)th^{3}(th(x)) - 14th^{2}(th(x))th^{2}(x) + 18th^{4}(th(x))th^{2}(x) - 18th^{4}(th(x))th^{4}(x) + 8th^{2}(th(x))th^{4}(x) - 6th^{6}(x)th^{2}(th(x)) + 6th^{6}(x)th^{4}(th(x)) + 4th(x)th(th(x)) - 2th^{2}(th(x))th^{6}(x) + 14th^{2}(x) + 2th^{6}(x) - 12th^{4}(x) + 10th^{2}(th(x)) - 6th^{4}(th(x)) - 4\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 18th^{2}(x)th^{2}(th(x)) + 22th^{4}(x)th^{2}(th(x)) + 8th(th(x))th(x) - 20th^{3}(x)th(th(x)) - 12th^{3}(th(x))th(x) + 20th^{3}(x)th^{3}(th(x)) - 4th(th(x))th^{3}(x) + 12th^{5}(x)th(th(x)) + 4th^{3}(th(x))th^{3}(x) - 12th^{5}(x)th^{3}(th(x)) - 14th^{2}(th(x))th^{2}(x) + 18th^{4}(th(x))th^{2}(x) - 18th^{4}(th(x))th^{4}(x) + 8th^{2}(th(x))th^{4}(x) - 6th^{6}(x)th^{2}(th(x)) + 6th^{6}(x)th^{4}(th(x)) + 4th(x)th(th(x)) - 2th^{2}(th(x))th^{6}(x) + 14th^{2}(x) + 2th^{6}(x) - 12th^{4}(x) + 10th^{2}(th(x)) - 6th^{4}(th(x)) - 4\right)}{dx}\\=& - 18*2th(x)(1 - th^{2}(x))th^{2}(th(x)) - 18th^{2}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 22*4th^{3}(x)(1 - th^{2}(x))th^{2}(th(x)) + 22th^{4}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 8(1 - th^{2}(th(x)))(1 - th^{2}(x))th(x) + 8th(th(x))(1 - th^{2}(x)) - 20*3th^{2}(x)(1 - th^{2}(x))th(th(x)) - 20th^{3}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 12*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th(x) - 12th^{3}(th(x))(1 - th^{2}(x)) + 20*3th^{2}(x)(1 - th^{2}(x))th^{3}(th(x)) + 20th^{3}(x)*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 4(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{3}(x) - 4th(th(x))*3th^{2}(x)(1 - th^{2}(x)) + 12*5th^{4}(x)(1 - th^{2}(x))th(th(x)) + 12th^{5}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 4*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{3}(x) + 4th^{3}(th(x))*3th^{2}(x)(1 - th^{2}(x)) - 12*5th^{4}(x)(1 - th^{2}(x))th^{3}(th(x)) - 12th^{5}(x)*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 14*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) - 14th^{2}(th(x))*2th(x)(1 - th^{2}(x)) + 18*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) + 18th^{4}(th(x))*2th(x)(1 - th^{2}(x)) - 18*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{4}(x) - 18th^{4}(th(x))*4th^{3}(x)(1 - th^{2}(x)) + 8*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{4}(x) + 8th^{2}(th(x))*4th^{3}(x)(1 - th^{2}(x)) - 6*6th^{5}(x)(1 - th^{2}(x))th^{2}(th(x)) - 6th^{6}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 6*6th^{5}(x)(1 - th^{2}(x))th^{4}(th(x)) + 6th^{6}(x)*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 4(1 - th^{2}(x))th(th(x)) + 4th(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{6}(x) - 2th^{2}(th(x))*6th^{5}(x)(1 - th^{2}(x)) + 14*2th(x)(1 - th^{2}(x)) + 2*6th^{5}(x)(1 - th^{2}(x)) - 12*4th^{3}(x)(1 - th^{2}(x)) + 10*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 6*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 0\\=& - 40th(x)th^{2}(th(x)) + 216th^{3}(x)th^{2}(th(x)) - 76th(th(x))th^{2}(x) + 196th^{4}(x)th(th(x)) + 168th^{3}(th(x))th^{2}(x) - 240th^{4}(x)th^{3}(th(x)) - 244th^{5}(x)th^{2}(th(x)) + 60th(th(x))th^{4}(x) - 120th^{6}(x)th(th(x)) - 160th^{3}(th(x))th^{4}(x) + 176th^{6}(x)th^{3}(th(x)) - 72th^{2}(th(x))th(x) + 72th^{4}(th(x))th(x) - 180th^{4}(th(x))th^{3}(x) - 92th^{2}(x)th(th(x)) + 96th^{2}(x)th^{3}(th(x)) + 112th^{2}(th(x))th^{3}(x) + 168th^{5}(x)th^{4}(th(x)) + 48th^{4}(th(x))th^{5}(x) - 68th^{2}(th(x))th^{5}(x) + 84th^{7}(x)th^{2}(th(x)) - 72th^{7}(x)th^{4}(th(x)) - 96th^{5}(th(x))th^{2}(x) + 144th^{5}(th(x))th^{4}(x) - 96th^{5}(th(x))th^{6}(x) - 36th^{3}(x)th^{4}(th(x)) + 56th^{3}(th(x))th^{6}(x) - 16th(th(x))th^{6}(x) + 16th^{8}(x)th(th(x)) - 36th^{8}(x)th^{3}(th(x)) + 24th^{8}(x)th^{5}(th(x)) - 4th^{3}(th(x))th^{8}(x) + 12th^{2}(th(x))th^{7}(x) + 96th^{5}(x) + 32th(th(x)) - 24th^{7}(x) - 112th^{3}(x) + 40th(x) - 56th^{3}(th(x)) + 24th^{5}(th(x))\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数th(th(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( th(th(x))\right)}{dx}\\=&(1 - th^{2}(th(x)))(1 - th^{2}(x))\\=&th^{2}(x)th^{2}(th(x)) - th^{2}(th(x)) - th^{2}(x) + 1\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( th^{2}(x)th^{2}(th(x)) - th^{2}(th(x)) - th^{2}(x) + 1\right)}{dx}\\=&2th(x)(1 - th^{2}(x))th^{2}(th(x)) + th^{2}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2th(x)(1 - th^{2}(x)) + 0\\=&2th(x)th^{2}(th(x)) - 2th^{3}(x)th^{2}(th(x)) + 2th(th(x))th^{2}(x) - 2th^{4}(x)th(th(x)) - 4th^{3}(th(x))th^{2}(x) + 2th^{4}(x)th^{3}(th(x)) + 2th^{2}(x)th(th(x)) - 2th(th(x)) + 2th^{3}(th(x)) - 2th(x) + 2th^{3}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2th(x)th^{2}(th(x)) - 2th^{3}(x)th^{2}(th(x)) + 2th(th(x))th^{2}(x) - 2th^{4}(x)th(th(x)) - 4th^{3}(th(x))th^{2}(x) + 2th^{4}(x)th^{3}(th(x)) + 2th^{2}(x)th(th(x)) - 2th(th(x)) + 2th^{3}(th(x)) - 2th(x) + 2th^{3}(x)\right)}{dx}\\=&2(1 - th^{2}(x))th^{2}(th(x)) + 2th(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2*3th^{2}(x)(1 - th^{2}(x))th^{2}(th(x)) - 2th^{3}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 2(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) + 2th(th(x))*2th(x)(1 - th^{2}(x)) - 2*4th^{3}(x)(1 - th^{2}(x))th(th(x)) - 2th^{4}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 4*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) - 4th^{3}(th(x))*2th(x)(1 - th^{2}(x)) + 2*4th^{3}(x)(1 - th^{2}(x))th^{3}(th(x)) + 2th^{4}(x)*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 2*2th(x)(1 - th^{2}(x))th(th(x)) + 2th^{2}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 2*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2(1 - th^{2}(x)) + 2*3th^{2}(x)(1 - th^{2}(x))\\=& - 18th^{2}(x)th^{2}(th(x)) + 22th^{4}(x)th^{2}(th(x)) + 8th(th(x))th(x) - 20th^{3}(x)th(th(x)) - 12th^{3}(th(x))th(x) + 20th^{3}(x)th^{3}(th(x)) - 4th(th(x))th^{3}(x) + 12th^{5}(x)th(th(x)) + 4th^{3}(th(x))th^{3}(x) - 12th^{5}(x)th^{3}(th(x)) - 14th^{2}(th(x))th^{2}(x) + 18th^{4}(th(x))th^{2}(x) - 18th^{4}(th(x))th^{4}(x) + 8th^{2}(th(x))th^{4}(x) - 6th^{6}(x)th^{2}(th(x)) + 6th^{6}(x)th^{4}(th(x)) + 4th(x)th(th(x)) - 2th^{2}(th(x))th^{6}(x) + 14th^{2}(x) + 2th^{6}(x) - 12th^{4}(x) + 10th^{2}(th(x)) - 6th^{4}(th(x)) - 4\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 18th^{2}(x)th^{2}(th(x)) + 22th^{4}(x)th^{2}(th(x)) + 8th(th(x))th(x) - 20th^{3}(x)th(th(x)) - 12th^{3}(th(x))th(x) + 20th^{3}(x)th^{3}(th(x)) - 4th(th(x))th^{3}(x) + 12th^{5}(x)th(th(x)) + 4th^{3}(th(x))th^{3}(x) - 12th^{5}(x)th^{3}(th(x)) - 14th^{2}(th(x))th^{2}(x) + 18th^{4}(th(x))th^{2}(x) - 18th^{4}(th(x))th^{4}(x) + 8th^{2}(th(x))th^{4}(x) - 6th^{6}(x)th^{2}(th(x)) + 6th^{6}(x)th^{4}(th(x)) + 4th(x)th(th(x)) - 2th^{2}(th(x))th^{6}(x) + 14th^{2}(x) + 2th^{6}(x) - 12th^{4}(x) + 10th^{2}(th(x)) - 6th^{4}(th(x)) - 4\right)}{dx}\\=& - 18*2th(x)(1 - th^{2}(x))th^{2}(th(x)) - 18th^{2}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 22*4th^{3}(x)(1 - th^{2}(x))th^{2}(th(x)) + 22th^{4}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 8(1 - th^{2}(th(x)))(1 - th^{2}(x))th(x) + 8th(th(x))(1 - th^{2}(x)) - 20*3th^{2}(x)(1 - th^{2}(x))th(th(x)) - 20th^{3}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 12*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th(x) - 12th^{3}(th(x))(1 - th^{2}(x)) + 20*3th^{2}(x)(1 - th^{2}(x))th^{3}(th(x)) + 20th^{3}(x)*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 4(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{3}(x) - 4th(th(x))*3th^{2}(x)(1 - th^{2}(x)) + 12*5th^{4}(x)(1 - th^{2}(x))th(th(x)) + 12th^{5}(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 4*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{3}(x) + 4th^{3}(th(x))*3th^{2}(x)(1 - th^{2}(x)) - 12*5th^{4}(x)(1 - th^{2}(x))th^{3}(th(x)) - 12th^{5}(x)*3th^{2}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 14*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) - 14th^{2}(th(x))*2th(x)(1 - th^{2}(x)) + 18*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{2}(x) + 18th^{4}(th(x))*2th(x)(1 - th^{2}(x)) - 18*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{4}(x) - 18th^{4}(th(x))*4th^{3}(x)(1 - th^{2}(x)) + 8*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{4}(x) + 8th^{2}(th(x))*4th^{3}(x)(1 - th^{2}(x)) - 6*6th^{5}(x)(1 - th^{2}(x))th^{2}(th(x)) - 6th^{6}(x)*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 6*6th^{5}(x)(1 - th^{2}(x))th^{4}(th(x)) + 6th^{6}(x)*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 4(1 - th^{2}(x))th(th(x)) + 4th(x)(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 2*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x))th^{6}(x) - 2th^{2}(th(x))*6th^{5}(x)(1 - th^{2}(x)) + 14*2th(x)(1 - th^{2}(x)) + 2*6th^{5}(x)(1 - th^{2}(x)) - 12*4th^{3}(x)(1 - th^{2}(x)) + 10*2th(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) - 6*4th^{3}(th(x))(1 - th^{2}(th(x)))(1 - th^{2}(x)) + 0\\=& - 40th(x)th^{2}(th(x)) + 216th^{3}(x)th^{2}(th(x)) - 76th(th(x))th^{2}(x) + 196th^{4}(x)th(th(x)) + 168th^{3}(th(x))th^{2}(x) - 240th^{4}(x)th^{3}(th(x)) - 244th^{5}(x)th^{2}(th(x)) + 60th(th(x))th^{4}(x) - 120th^{6}(x)th(th(x)) - 160th^{3}(th(x))th^{4}(x) + 176th^{6}(x)th^{3}(th(x)) - 72th^{2}(th(x))th(x) + 72th^{4}(th(x))th(x) - 180th^{4}(th(x))th^{3}(x) - 92th^{2}(x)th(th(x)) + 96th^{2}(x)th^{3}(th(x)) + 112th^{2}(th(x))th^{3}(x) + 168th^{5}(x)th^{4}(th(x)) + 48th^{4}(th(x))th^{5}(x) - 68th^{2}(th(x))th^{5}(x) + 84th^{7}(x)th^{2}(th(x)) - 72th^{7}(x)th^{4}(th(x)) - 96th^{5}(th(x))th^{2}(x) + 144th^{5}(th(x))th^{4}(x) - 96th^{5}(th(x))th^{6}(x) - 36th^{3}(x)th^{4}(th(x)) + 56th^{3}(th(x))th^{6}(x) - 16th(th(x))th^{6}(x) + 16th^{8}(x)th(th(x)) - 36th^{8}(x)th^{3}(th(x)) + 24th^{8}(x)th^{5}(th(x)) - 4th^{3}(th(x))th^{8}(x) + 12th^{2}(th(x))th^{7}(x) + 96th^{5}(x) + 32th(th(x)) - 24th^{7}(x) - 112th^{3}(x) + 40th(x) - 56th^{3}(th(x)) + 24th^{5}(th(x))\\ \end{split}\end{equation} \]
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