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。
\[ \begin{equation}\begin{split}【1/1】求函数In(xsin(x + tan(x))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = Inxsin(x + tan(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( Inxsin(x + tan(x))\right)}{dx}\\=&Insin(x + tan(x)) + Inxcos(x + tan(x))(1 + sec^{2}(x)(1))\\=&Insin(x + tan(x)) + Inxcos(x + tan(x))sec^{2}(x) + Inxcos(x + tan(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( Insin(x + tan(x)) + Inxcos(x + tan(x))sec^{2}(x) + Inxcos(x + tan(x))\right)}{dx}\\=&Incos(x + tan(x))(1 + sec^{2}(x)(1)) + Incos(x + tan(x))sec^{2}(x) + Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) + Inxcos(x + tan(x))*2sec^{2}(x)tan(x) + Incos(x + tan(x)) + Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))\\=&2Incos(x + tan(x))sec^{2}(x) + 2Incos(x + tan(x)) - 2Inxsin(x + tan(x))sec^{2}(x) - Inxsin(x + tan(x))sec^{4}(x) + 2Inxcos(x + tan(x))tan(x)sec^{2}(x) - Inxsin(x + tan(x))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2Incos(x + tan(x))sec^{2}(x) + 2Incos(x + tan(x)) - 2Inxsin(x + tan(x))sec^{2}(x) - Inxsin(x + tan(x))sec^{4}(x) + 2Inxcos(x + tan(x))tan(x)sec^{2}(x) - Inxsin(x + tan(x))\right)}{dx}\\=&2In*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) + 2Incos(x + tan(x))*2sec^{2}(x)tan(x) + 2In*-sin(x + tan(x))(1 + sec^{2}(x)(1)) - 2Insin(x + tan(x))sec^{2}(x) - 2Inxcos(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) - 2Inxsin(x + tan(x))*2sec^{2}(x)tan(x) - Insin(x + tan(x))sec^{4}(x) - Inxcos(x + tan(x))(1 + sec^{2}(x)(1))sec^{4}(x) - Inxsin(x + tan(x))*4sec^{4}(x)tan(x) + 2Incos(x + tan(x))tan(x)sec^{2}(x) + 2Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{2}(x) + 2Inxcos(x + tan(x))sec^{2}(x)(1)sec^{2}(x) + 2Inxcos(x + tan(x))tan(x)*2sec^{2}(x)tan(x) - Insin(x + tan(x)) - Inxcos(x + tan(x))(1 + sec^{2}(x)(1))\\=&-6Insin(x + tan(x))sec^{2}(x) - 3Insin(x + tan(x))sec^{4}(x) + 6Incos(x + tan(x))tan(x)sec^{2}(x) - 3Insin(x + tan(x)) - Inxcos(x + tan(x))sec^{4}(x) - 6Inxsin(x + tan(x))tan(x)sec^{2}(x) - Inxcos(x + tan(x))sec^{6}(x) - 6Inxsin(x + tan(x))tan(x)sec^{4}(x) - 3Inxcos(x + tan(x))sec^{2}(x) + 4Inxcos(x + tan(x))tan^{2}(x)sec^{2}(x) - Inxcos(x + tan(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -6Insin(x + tan(x))sec^{2}(x) - 3Insin(x + tan(x))sec^{4}(x) + 6Incos(x + tan(x))tan(x)sec^{2}(x) - 3Insin(x + tan(x)) - Inxcos(x + tan(x))sec^{4}(x) - 6Inxsin(x + tan(x))tan(x)sec^{2}(x) - Inxcos(x + tan(x))sec^{6}(x) - 6Inxsin(x + tan(x))tan(x)sec^{4}(x) - 3Inxcos(x + tan(x))sec^{2}(x) + 4Inxcos(x + tan(x))tan^{2}(x)sec^{2}(x) - Inxcos(x + tan(x))\right)}{dx}\\=&-6Incos(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) - 6Insin(x + tan(x))*2sec^{2}(x)tan(x) - 3Incos(x + tan(x))(1 + sec^{2}(x)(1))sec^{4}(x) - 3Insin(x + tan(x))*4sec^{4}(x)tan(x) + 6In*-sin(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{2}(x) + 6Incos(x + tan(x))sec^{2}(x)(1)sec^{2}(x) + 6Incos(x + tan(x))tan(x)*2sec^{2}(x)tan(x) - 3Incos(x + tan(x))(1 + sec^{2}(x)(1)) - Incos(x + tan(x))sec^{4}(x) - Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{4}(x) - Inxcos(x + tan(x))*4sec^{4}(x)tan(x) - 6Insin(x + tan(x))tan(x)sec^{2}(x) - 6Inxcos(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{2}(x) - 6Inxsin(x + tan(x))sec^{2}(x)(1)sec^{2}(x) - 6Inxsin(x + tan(x))tan(x)*2sec^{2}(x)tan(x) - Incos(x + tan(x))sec^{6}(x) - Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{6}(x) - Inxcos(x + tan(x))*6sec^{6}(x)tan(x) - 6Insin(x + tan(x))tan(x)sec^{4}(x) - 6Inxcos(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{4}(x) - 6Inxsin(x + tan(x))sec^{2}(x)(1)sec^{4}(x) - 6Inxsin(x + tan(x))tan(x)*4sec^{4}(x)tan(x) - 3Incos(x + tan(x))sec^{2}(x) - 3Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) - 3Inxcos(x + tan(x))*2sec^{2}(x)tan(x) + 4Incos(x + tan(x))tan^{2}(x)sec^{2}(x) + 4Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))tan^{2}(x)sec^{2}(x) + 4Inxcos(x + tan(x))*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4Inxcos(x + tan(x))tan^{2}(x)*2sec^{2}(x)tan(x) - Incos(x + tan(x)) - Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))\\=& - 4Incos(x + tan(x))sec^{4}(x) - 24Insin(x + tan(x))tan(x)sec^{2}(x) - 4Incos(x + tan(x))sec^{6}(x) - 24Insin(x + tan(x))tan(x)sec^{4}(x) - 12Incos(x + tan(x))sec^{2}(x) + 16Incos(x + tan(x))tan^{2}(x)sec^{2}(x) - 4Incos(x + tan(x)) - 2Inxsin(x + tan(x))sec^{4}(x) - 4Inxsin(x + tan(x))sec^{6}(x) - 8Inxcos(x + tan(x))tan(x)sec^{4}(x) - 12Inxcos(x + tan(x))tan(x)sec^{2}(x) - 12Inxcos(x + tan(x))tan(x)sec^{6}(x) - 16Inxsin(x + tan(x))tan^{2}(x)sec^{2}(x) + Inxsin(x + tan(x))sec^{8}(x) - 28Inxsin(x + tan(x))tan^{2}(x)sec^{4}(x) + 4Inxsin(x + tan(x))sec^{2}(x) + 8Inxcos(x + tan(x))tan^{3}(x)sec^{2}(x) + Inxsin(x + tan(x))\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数In(xsin(x + tan(x))) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = Inxsin(x + tan(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( Inxsin(x + tan(x))\right)}{dx}\\=&Insin(x + tan(x)) + Inxcos(x + tan(x))(1 + sec^{2}(x)(1))\\=&Insin(x + tan(x)) + Inxcos(x + tan(x))sec^{2}(x) + Inxcos(x + tan(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( Insin(x + tan(x)) + Inxcos(x + tan(x))sec^{2}(x) + Inxcos(x + tan(x))\right)}{dx}\\=&Incos(x + tan(x))(1 + sec^{2}(x)(1)) + Incos(x + tan(x))sec^{2}(x) + Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) + Inxcos(x + tan(x))*2sec^{2}(x)tan(x) + Incos(x + tan(x)) + Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))\\=&2Incos(x + tan(x))sec^{2}(x) + 2Incos(x + tan(x)) - 2Inxsin(x + tan(x))sec^{2}(x) - Inxsin(x + tan(x))sec^{4}(x) + 2Inxcos(x + tan(x))tan(x)sec^{2}(x) - Inxsin(x + tan(x))\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2Incos(x + tan(x))sec^{2}(x) + 2Incos(x + tan(x)) - 2Inxsin(x + tan(x))sec^{2}(x) - Inxsin(x + tan(x))sec^{4}(x) + 2Inxcos(x + tan(x))tan(x)sec^{2}(x) - Inxsin(x + tan(x))\right)}{dx}\\=&2In*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) + 2Incos(x + tan(x))*2sec^{2}(x)tan(x) + 2In*-sin(x + tan(x))(1 + sec^{2}(x)(1)) - 2Insin(x + tan(x))sec^{2}(x) - 2Inxcos(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) - 2Inxsin(x + tan(x))*2sec^{2}(x)tan(x) - Insin(x + tan(x))sec^{4}(x) - Inxcos(x + tan(x))(1 + sec^{2}(x)(1))sec^{4}(x) - Inxsin(x + tan(x))*4sec^{4}(x)tan(x) + 2Incos(x + tan(x))tan(x)sec^{2}(x) + 2Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{2}(x) + 2Inxcos(x + tan(x))sec^{2}(x)(1)sec^{2}(x) + 2Inxcos(x + tan(x))tan(x)*2sec^{2}(x)tan(x) - Insin(x + tan(x)) - Inxcos(x + tan(x))(1 + sec^{2}(x)(1))\\=&-6Insin(x + tan(x))sec^{2}(x) - 3Insin(x + tan(x))sec^{4}(x) + 6Incos(x + tan(x))tan(x)sec^{2}(x) - 3Insin(x + tan(x)) - Inxcos(x + tan(x))sec^{4}(x) - 6Inxsin(x + tan(x))tan(x)sec^{2}(x) - Inxcos(x + tan(x))sec^{6}(x) - 6Inxsin(x + tan(x))tan(x)sec^{4}(x) - 3Inxcos(x + tan(x))sec^{2}(x) + 4Inxcos(x + tan(x))tan^{2}(x)sec^{2}(x) - Inxcos(x + tan(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -6Insin(x + tan(x))sec^{2}(x) - 3Insin(x + tan(x))sec^{4}(x) + 6Incos(x + tan(x))tan(x)sec^{2}(x) - 3Insin(x + tan(x)) - Inxcos(x + tan(x))sec^{4}(x) - 6Inxsin(x + tan(x))tan(x)sec^{2}(x) - Inxcos(x + tan(x))sec^{6}(x) - 6Inxsin(x + tan(x))tan(x)sec^{4}(x) - 3Inxcos(x + tan(x))sec^{2}(x) + 4Inxcos(x + tan(x))tan^{2}(x)sec^{2}(x) - Inxcos(x + tan(x))\right)}{dx}\\=&-6Incos(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) - 6Insin(x + tan(x))*2sec^{2}(x)tan(x) - 3Incos(x + tan(x))(1 + sec^{2}(x)(1))sec^{4}(x) - 3Insin(x + tan(x))*4sec^{4}(x)tan(x) + 6In*-sin(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{2}(x) + 6Incos(x + tan(x))sec^{2}(x)(1)sec^{2}(x) + 6Incos(x + tan(x))tan(x)*2sec^{2}(x)tan(x) - 3Incos(x + tan(x))(1 + sec^{2}(x)(1)) - Incos(x + tan(x))sec^{4}(x) - Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{4}(x) - Inxcos(x + tan(x))*4sec^{4}(x)tan(x) - 6Insin(x + tan(x))tan(x)sec^{2}(x) - 6Inxcos(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{2}(x) - 6Inxsin(x + tan(x))sec^{2}(x)(1)sec^{2}(x) - 6Inxsin(x + tan(x))tan(x)*2sec^{2}(x)tan(x) - Incos(x + tan(x))sec^{6}(x) - Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{6}(x) - Inxcos(x + tan(x))*6sec^{6}(x)tan(x) - 6Insin(x + tan(x))tan(x)sec^{4}(x) - 6Inxcos(x + tan(x))(1 + sec^{2}(x)(1))tan(x)sec^{4}(x) - 6Inxsin(x + tan(x))sec^{2}(x)(1)sec^{4}(x) - 6Inxsin(x + tan(x))tan(x)*4sec^{4}(x)tan(x) - 3Incos(x + tan(x))sec^{2}(x) - 3Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))sec^{2}(x) - 3Inxcos(x + tan(x))*2sec^{2}(x)tan(x) + 4Incos(x + tan(x))tan^{2}(x)sec^{2}(x) + 4Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))tan^{2}(x)sec^{2}(x) + 4Inxcos(x + tan(x))*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 4Inxcos(x + tan(x))tan^{2}(x)*2sec^{2}(x)tan(x) - Incos(x + tan(x)) - Inx*-sin(x + tan(x))(1 + sec^{2}(x)(1))\\=& - 4Incos(x + tan(x))sec^{4}(x) - 24Insin(x + tan(x))tan(x)sec^{2}(x) - 4Incos(x + tan(x))sec^{6}(x) - 24Insin(x + tan(x))tan(x)sec^{4}(x) - 12Incos(x + tan(x))sec^{2}(x) + 16Incos(x + tan(x))tan^{2}(x)sec^{2}(x) - 4Incos(x + tan(x)) - 2Inxsin(x + tan(x))sec^{4}(x) - 4Inxsin(x + tan(x))sec^{6}(x) - 8Inxcos(x + tan(x))tan(x)sec^{4}(x) - 12Inxcos(x + tan(x))tan(x)sec^{2}(x) - 12Inxcos(x + tan(x))tan(x)sec^{6}(x) - 16Inxsin(x + tan(x))tan^{2}(x)sec^{2}(x) + Inxsin(x + tan(x))sec^{8}(x) - 28Inxsin(x + tan(x))tan^{2}(x)sec^{4}(x) + 4Inxsin(x + tan(x))sec^{2}(x) + 8Inxcos(x + tan(x))tan^{3}(x)sec^{2}(x) + Inxsin(x + tan(x))\\ \end{split}\end{equation} \]
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