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。
\[ \begin{equation}\begin{split}【1/1】求函数sin(xx + lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(x^{2} + lg(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(x^{2} + lg(x))\right)}{dx}\\=&cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})\\=&2xcos(x^{2} + lg(x)) + \frac{cos(x^{2} + lg(x))}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2xcos(x^{2} + lg(x)) + \frac{cos(x^{2} + lg(x))}{xln{10}}\right)}{dx}\\=&2cos(x^{2} + lg(x)) + 2x*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) + \frac{-cos(x^{2} + lg(x))}{x^{2}ln{10}} + \frac{-0cos(x^{2} + lg(x))}{xln^{2}{10}} + \frac{-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{xln{10}}\\=&2cos(x^{2} + lg(x)) - 4x^{2}sin(x^{2} + lg(x)) - \frac{4sin(x^{2} + lg(x))}{ln{10}} - \frac{cos(x^{2} + lg(x))}{x^{2}ln{10}} - \frac{sin(x^{2} + lg(x))}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2cos(x^{2} + lg(x)) - 4x^{2}sin(x^{2} + lg(x)) - \frac{4sin(x^{2} + lg(x))}{ln{10}} - \frac{cos(x^{2} + lg(x))}{x^{2}ln{10}} - \frac{sin(x^{2} + lg(x))}{x^{2}ln^{2}{10}}\right)}{dx}\\=&2*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - 4*2xsin(x^{2} + lg(x)) - 4x^{2}cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - \frac{4*-0sin(x^{2} + lg(x))}{ln^{2}{10}} - \frac{4cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{ln{10}} - \frac{-2cos(x^{2} + lg(x))}{x^{3}ln{10}} - \frac{-0cos(x^{2} + lg(x))}{x^{2}ln^{2}{10}} - \frac{-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{2}ln{10}} - \frac{-2sin(x^{2} + lg(x))}{x^{3}ln^{2}{10}} - \frac{-2*0sin(x^{2} + lg(x))}{x^{2}ln^{3}{10}} - \frac{cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{2}ln^{2}{10}}\\=&-12xsin(x^{2} + lg(x)) - 8x^{3}cos(x^{2} + lg(x)) - \frac{12xcos(x^{2} + lg(x))}{ln{10}} - \frac{6cos(x^{2} + lg(x))}{xln^{2}{10}} + \frac{2cos(x^{2} + lg(x))}{x^{3}ln{10}} + \frac{3sin(x^{2} + lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(x^{2} + lg(x))}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -12xsin(x^{2} + lg(x)) - 8x^{3}cos(x^{2} + lg(x)) - \frac{12xcos(x^{2} + lg(x))}{ln{10}} - \frac{6cos(x^{2} + lg(x))}{xln^{2}{10}} + \frac{2cos(x^{2} + lg(x))}{x^{3}ln{10}} + \frac{3sin(x^{2} + lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(x^{2} + lg(x))}{x^{3}ln^{3}{10}}\right)}{dx}\\=&-12sin(x^{2} + lg(x)) - 12xcos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - 8*3x^{2}cos(x^{2} + lg(x)) - 8x^{3}*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - \frac{12cos(x^{2} + lg(x))}{ln{10}} - \frac{12x*-0cos(x^{2} + lg(x))}{ln^{2}{10}} - \frac{12x*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{ln{10}} - \frac{6*-cos(x^{2} + lg(x))}{x^{2}ln^{2}{10}} - \frac{6*-2*0cos(x^{2} + lg(x))}{xln^{3}{10}} - \frac{6*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{xln^{2}{10}} + \frac{2*-3cos(x^{2} + lg(x))}{x^{4}ln{10}} + \frac{2*-0cos(x^{2} + lg(x))}{x^{3}ln^{2}{10}} + \frac{2*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{3}ln{10}} + \frac{3*-3sin(x^{2} + lg(x))}{x^{4}ln^{2}{10}} + \frac{3*-2*0sin(x^{2} + lg(x))}{x^{3}ln^{3}{10}} + \frac{3cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{3}ln^{2}{10}} - \frac{-3cos(x^{2} + lg(x))}{x^{4}ln^{3}{10}} - \frac{-3*0cos(x^{2} + lg(x))}{x^{3}ln^{4}{10}} - \frac{-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{3}ln^{3}{10}}\\=&-12sin(x^{2} + lg(x)) - 48x^{2}cos(x^{2} + lg(x)) - \frac{24cos(x^{2} + lg(x))}{ln{10}} + 16x^{4}sin(x^{2} + lg(x)) + \frac{32x^{2}sin(x^{2} + lg(x))}{ln{10}} + \frac{24sin(x^{2} + lg(x))}{ln^{2}{10}} + \frac{12cos(x^{2} + lg(x))}{x^{2}ln^{2}{10}} + \frac{8sin(x^{2} + lg(x))}{x^{2}ln^{3}{10}} - \frac{6cos(x^{2} + lg(x))}{x^{4}ln{10}} - \frac{4sin(x^{2} + lg(x))}{x^{2}ln{10}} - \frac{11sin(x^{2} + lg(x))}{x^{4}ln^{2}{10}} + \frac{6cos(x^{2} + lg(x))}{x^{4}ln^{3}{10}} + \frac{sin(x^{2} + lg(x))}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sin(xx + lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin(x^{2} + lg(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(x^{2} + lg(x))\right)}{dx}\\=&cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})\\=&2xcos(x^{2} + lg(x)) + \frac{cos(x^{2} + lg(x))}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2xcos(x^{2} + lg(x)) + \frac{cos(x^{2} + lg(x))}{xln{10}}\right)}{dx}\\=&2cos(x^{2} + lg(x)) + 2x*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) + \frac{-cos(x^{2} + lg(x))}{x^{2}ln{10}} + \frac{-0cos(x^{2} + lg(x))}{xln^{2}{10}} + \frac{-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{xln{10}}\\=&2cos(x^{2} + lg(x)) - 4x^{2}sin(x^{2} + lg(x)) - \frac{4sin(x^{2} + lg(x))}{ln{10}} - \frac{cos(x^{2} + lg(x))}{x^{2}ln{10}} - \frac{sin(x^{2} + lg(x))}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2cos(x^{2} + lg(x)) - 4x^{2}sin(x^{2} + lg(x)) - \frac{4sin(x^{2} + lg(x))}{ln{10}} - \frac{cos(x^{2} + lg(x))}{x^{2}ln{10}} - \frac{sin(x^{2} + lg(x))}{x^{2}ln^{2}{10}}\right)}{dx}\\=&2*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - 4*2xsin(x^{2} + lg(x)) - 4x^{2}cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - \frac{4*-0sin(x^{2} + lg(x))}{ln^{2}{10}} - \frac{4cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{ln{10}} - \frac{-2cos(x^{2} + lg(x))}{x^{3}ln{10}} - \frac{-0cos(x^{2} + lg(x))}{x^{2}ln^{2}{10}} - \frac{-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{2}ln{10}} - \frac{-2sin(x^{2} + lg(x))}{x^{3}ln^{2}{10}} - \frac{-2*0sin(x^{2} + lg(x))}{x^{2}ln^{3}{10}} - \frac{cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{2}ln^{2}{10}}\\=&-12xsin(x^{2} + lg(x)) - 8x^{3}cos(x^{2} + lg(x)) - \frac{12xcos(x^{2} + lg(x))}{ln{10}} - \frac{6cos(x^{2} + lg(x))}{xln^{2}{10}} + \frac{2cos(x^{2} + lg(x))}{x^{3}ln{10}} + \frac{3sin(x^{2} + lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(x^{2} + lg(x))}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -12xsin(x^{2} + lg(x)) - 8x^{3}cos(x^{2} + lg(x)) - \frac{12xcos(x^{2} + lg(x))}{ln{10}} - \frac{6cos(x^{2} + lg(x))}{xln^{2}{10}} + \frac{2cos(x^{2} + lg(x))}{x^{3}ln{10}} + \frac{3sin(x^{2} + lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(x^{2} + lg(x))}{x^{3}ln^{3}{10}}\right)}{dx}\\=&-12sin(x^{2} + lg(x)) - 12xcos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - 8*3x^{2}cos(x^{2} + lg(x)) - 8x^{3}*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)}) - \frac{12cos(x^{2} + lg(x))}{ln{10}} - \frac{12x*-0cos(x^{2} + lg(x))}{ln^{2}{10}} - \frac{12x*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{ln{10}} - \frac{6*-cos(x^{2} + lg(x))}{x^{2}ln^{2}{10}} - \frac{6*-2*0cos(x^{2} + lg(x))}{xln^{3}{10}} - \frac{6*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{xln^{2}{10}} + \frac{2*-3cos(x^{2} + lg(x))}{x^{4}ln{10}} + \frac{2*-0cos(x^{2} + lg(x))}{x^{3}ln^{2}{10}} + \frac{2*-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{3}ln{10}} + \frac{3*-3sin(x^{2} + lg(x))}{x^{4}ln^{2}{10}} + \frac{3*-2*0sin(x^{2} + lg(x))}{x^{3}ln^{3}{10}} + \frac{3cos(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{3}ln^{2}{10}} - \frac{-3cos(x^{2} + lg(x))}{x^{4}ln^{3}{10}} - \frac{-3*0cos(x^{2} + lg(x))}{x^{3}ln^{4}{10}} - \frac{-sin(x^{2} + lg(x))(2x + \frac{1}{ln{10}(x)})}{x^{3}ln^{3}{10}}\\=&-12sin(x^{2} + lg(x)) - 48x^{2}cos(x^{2} + lg(x)) - \frac{24cos(x^{2} + lg(x))}{ln{10}} + 16x^{4}sin(x^{2} + lg(x)) + \frac{32x^{2}sin(x^{2} + lg(x))}{ln{10}} + \frac{24sin(x^{2} + lg(x))}{ln^{2}{10}} + \frac{12cos(x^{2} + lg(x))}{x^{2}ln^{2}{10}} + \frac{8sin(x^{2} + lg(x))}{x^{2}ln^{3}{10}} - \frac{6cos(x^{2} + lg(x))}{x^{4}ln{10}} - \frac{4sin(x^{2} + lg(x))}{x^{2}ln{10}} - \frac{11sin(x^{2} + lg(x))}{x^{4}ln^{2}{10}} + \frac{6cos(x^{2} + lg(x))}{x^{4}ln^{3}{10}} + \frac{sin(x^{2} + lg(x))}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
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