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。
\[ \begin{equation}\begin{split}【1/1】求函数12345sin(x)cos(x)tan(x)lg(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 12345lg(x)sin(x)cos(x)tan(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 12345lg(x)sin(x)cos(x)tan(x)\right)}{dx}\\=&\frac{12345sin(x)cos(x)tan(x)}{ln{10}(x)} + 12345lg(x)cos(x)cos(x)tan(x) + 12345lg(x)sin(x)*-sin(x)tan(x) + 12345lg(x)sin(x)cos(x)sec^{2}(x)(1)\\=&\frac{12345sin(x)cos(x)tan(x)}{xln{10}} + 12345lg(x)cos^{2}(x)tan(x) - 12345lg(x)sin^{2}(x)tan(x) + 12345lg(x)sin(x)cos(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{12345sin(x)cos(x)tan(x)}{xln{10}} + 12345lg(x)cos^{2}(x)tan(x) - 12345lg(x)sin^{2}(x)tan(x) + 12345lg(x)sin(x)cos(x)sec^{2}(x)\right)}{dx}\\=&\frac{12345*-sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{12345*-0sin(x)cos(x)tan(x)}{xln^{2}{10}} + \frac{12345cos(x)cos(x)tan(x)}{xln{10}} + \frac{12345sin(x)*-sin(x)tan(x)}{xln{10}} + \frac{12345sin(x)cos(x)sec^{2}(x)(1)}{xln{10}} + \frac{12345cos^{2}(x)tan(x)}{ln{10}(x)} + 12345lg(x)*-2cos(x)sin(x)tan(x) + 12345lg(x)cos^{2}(x)sec^{2}(x)(1) - \frac{12345sin^{2}(x)tan(x)}{ln{10}(x)} - 12345lg(x)*2sin(x)cos(x)tan(x) - 12345lg(x)sin^{2}(x)sec^{2}(x)(1) + \frac{12345sin(x)cos(x)sec^{2}(x)}{ln{10}(x)} + 12345lg(x)cos(x)cos(x)sec^{2}(x) + 12345lg(x)sin(x)*-sin(x)sec^{2}(x) + 12345lg(x)sin(x)cos(x)*2sec^{2}(x)tan(x)\\=&\frac{-12345sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{24690cos^{2}(x)tan(x)}{xln{10}} - \frac{24690sin^{2}(x)tan(x)}{xln{10}} + \frac{24690sin(x)cos(x)sec^{2}(x)}{xln{10}} + 24690lg(x)sin(x)cos(x)tan(x)sec^{2}(x) + 24690lg(x)cos^{2}(x)sec^{2}(x) - 49380lg(x)sin(x)cos(x)tan(x) - 24690lg(x)sin^{2}(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-12345sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{24690cos^{2}(x)tan(x)}{xln{10}} - \frac{24690sin^{2}(x)tan(x)}{xln{10}} + \frac{24690sin(x)cos(x)sec^{2}(x)}{xln{10}} + 24690lg(x)sin(x)cos(x)tan(x)sec^{2}(x) + 24690lg(x)cos^{2}(x)sec^{2}(x) - 49380lg(x)sin(x)cos(x)tan(x) - 24690lg(x)sin^{2}(x)sec^{2}(x)\right)}{dx}\\=&\frac{-12345*-2sin(x)cos(x)tan(x)}{x^{3}ln{10}} - \frac{12345*-0sin(x)cos(x)tan(x)}{x^{2}ln^{2}{10}} - \frac{12345cos(x)cos(x)tan(x)}{x^{2}ln{10}} - \frac{12345sin(x)*-sin(x)tan(x)}{x^{2}ln{10}} - \frac{12345sin(x)cos(x)sec^{2}(x)(1)}{x^{2}ln{10}} + \frac{24690*-cos^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{24690*-0cos^{2}(x)tan(x)}{xln^{2}{10}} + \frac{24690*-2cos(x)sin(x)tan(x)}{xln{10}} + \frac{24690cos^{2}(x)sec^{2}(x)(1)}{xln{10}} - \frac{24690*-sin^{2}(x)tan(x)}{x^{2}ln{10}} - \frac{24690*-0sin^{2}(x)tan(x)}{xln^{2}{10}} - \frac{24690*2sin(x)cos(x)tan(x)}{xln{10}} - \frac{24690sin^{2}(x)sec^{2}(x)(1)}{xln{10}} + \frac{24690*-sin(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{24690*-0sin(x)cos(x)sec^{2}(x)}{xln^{2}{10}} + \frac{24690cos(x)cos(x)sec^{2}(x)}{xln{10}} + \frac{24690sin(x)*-sin(x)sec^{2}(x)}{xln{10}} + \frac{24690sin(x)cos(x)*2sec^{2}(x)tan(x)}{xln{10}} + \frac{24690sin(x)cos(x)tan(x)sec^{2}(x)}{ln{10}(x)} + 24690lg(x)cos(x)cos(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)*-sin(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) + 24690lg(x)sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) + \frac{24690cos^{2}(x)sec^{2}(x)}{ln{10}(x)} + 24690lg(x)*-2cos(x)sin(x)sec^{2}(x) + 24690lg(x)cos^{2}(x)*2sec^{2}(x)tan(x) - \frac{49380sin(x)cos(x)tan(x)}{ln{10}(x)} - 49380lg(x)cos(x)cos(x)tan(x) - 49380lg(x)sin(x)*-sin(x)tan(x) - 49380lg(x)sin(x)cos(x)sec^{2}(x)(1) - \frac{24690sin^{2}(x)sec^{2}(x)}{ln{10}(x)} - 24690lg(x)*2sin(x)cos(x)sec^{2}(x) - 24690lg(x)sin^{2}(x)*2sec^{2}(x)tan(x)\\=&\frac{74070sin(x)cos(x)tan(x)sec^{2}(x)}{xln{10}} - \frac{37035cos^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{37035sin^{2}(x)tan(x)}{x^{2}ln{10}} - \frac{37035sin(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{24690sin(x)cos(x)tan(x)}{x^{3}ln{10}} + \frac{74070cos^{2}(x)sec^{2}(x)}{xln{10}} - \frac{74070sin^{2}(x)sec^{2}(x)}{xln{10}} - \frac{148140sin(x)cos(x)tan(x)}{xln{10}} + 74070lg(x)cos^{2}(x)tan(x)sec^{2}(x) - 74070lg(x)sin^{2}(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)cos(x)sec^{4}(x) + 49380lg(x)sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140lg(x)sin(x)cos(x)sec^{2}(x) - 49380lg(x)cos^{2}(x)tan(x) + 49380lg(x)sin^{2}(x)tan(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{74070sin(x)cos(x)tan(x)sec^{2}(x)}{xln{10}} - \frac{37035cos^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{37035sin^{2}(x)tan(x)}{x^{2}ln{10}} - \frac{37035sin(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{24690sin(x)cos(x)tan(x)}{x^{3}ln{10}} + \frac{74070cos^{2}(x)sec^{2}(x)}{xln{10}} - \frac{74070sin^{2}(x)sec^{2}(x)}{xln{10}} - \frac{148140sin(x)cos(x)tan(x)}{xln{10}} + 74070lg(x)cos^{2}(x)tan(x)sec^{2}(x) - 74070lg(x)sin^{2}(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)cos(x)sec^{4}(x) + 49380lg(x)sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140lg(x)sin(x)cos(x)sec^{2}(x) - 49380lg(x)cos^{2}(x)tan(x) + 49380lg(x)sin^{2}(x)tan(x)\right)}{dx}\\=&\frac{74070*-sin(x)cos(x)tan(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{74070*-0sin(x)cos(x)tan(x)sec^{2}(x)}{xln^{2}{10}} + \frac{74070cos(x)cos(x)tan(x)sec^{2}(x)}{xln{10}} + \frac{74070sin(x)*-sin(x)tan(x)sec^{2}(x)}{xln{10}} + \frac{74070sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x)}{xln{10}} + \frac{74070sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x)}{xln{10}} - \frac{37035*-2cos^{2}(x)tan(x)}{x^{3}ln{10}} - \frac{37035*-0cos^{2}(x)tan(x)}{x^{2}ln^{2}{10}} - \frac{37035*-2cos(x)sin(x)tan(x)}{x^{2}ln{10}} - \frac{37035cos^{2}(x)sec^{2}(x)(1)}{x^{2}ln{10}} + \frac{37035*-2sin^{2}(x)tan(x)}{x^{3}ln{10}} + \frac{37035*-0sin^{2}(x)tan(x)}{x^{2}ln^{2}{10}} + \frac{37035*2sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{37035sin^{2}(x)sec^{2}(x)(1)}{x^{2}ln{10}} - \frac{37035*-2sin(x)cos(x)sec^{2}(x)}{x^{3}ln{10}} - \frac{37035*-0sin(x)cos(x)sec^{2}(x)}{x^{2}ln^{2}{10}} - \frac{37035cos(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{37035sin(x)*-sin(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{37035sin(x)cos(x)*2sec^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{24690*-3sin(x)cos(x)tan(x)}{x^{4}ln{10}} + \frac{24690*-0sin(x)cos(x)tan(x)}{x^{3}ln^{2}{10}} + \frac{24690cos(x)cos(x)tan(x)}{x^{3}ln{10}} + \frac{24690sin(x)*-sin(x)tan(x)}{x^{3}ln{10}} + \frac{24690sin(x)cos(x)sec^{2}(x)(1)}{x^{3}ln{10}} + \frac{74070*-cos^{2}(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{74070*-0cos^{2}(x)sec^{2}(x)}{xln^{2}{10}} + \frac{74070*-2cos(x)sin(x)sec^{2}(x)}{xln{10}} + \frac{74070cos^{2}(x)*2sec^{2}(x)tan(x)}{xln{10}} - \frac{74070*-sin^{2}(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{74070*-0sin^{2}(x)sec^{2}(x)}{xln^{2}{10}} - \frac{74070*2sin(x)cos(x)sec^{2}(x)}{xln{10}} - \frac{74070sin^{2}(x)*2sec^{2}(x)tan(x)}{xln{10}} - \frac{148140*-sin(x)cos(x)tan(x)}{x^{2}ln{10}} - \frac{148140*-0sin(x)cos(x)tan(x)}{xln^{2}{10}} - \frac{148140cos(x)cos(x)tan(x)}{xln{10}} - \frac{148140sin(x)*-sin(x)tan(x)}{xln{10}} - \frac{148140sin(x)cos(x)sec^{2}(x)(1)}{xln{10}} + \frac{74070cos^{2}(x)tan(x)sec^{2}(x)}{ln{10}(x)} + 74070lg(x)*-2cos(x)sin(x)tan(x)sec^{2}(x) + 74070lg(x)cos^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 74070lg(x)cos^{2}(x)tan(x)*2sec^{2}(x)tan(x) - \frac{74070sin^{2}(x)tan(x)sec^{2}(x)}{ln{10}(x)} - 74070lg(x)*2sin(x)cos(x)tan(x)sec^{2}(x) - 74070lg(x)sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 74070lg(x)sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) + \frac{24690sin(x)cos(x)sec^{4}(x)}{ln{10}(x)} + 24690lg(x)cos(x)cos(x)sec^{4}(x) + 24690lg(x)sin(x)*-sin(x)sec^{4}(x) + 24690lg(x)sin(x)cos(x)*4sec^{4}(x)tan(x) + \frac{49380sin(x)cos(x)tan^{2}(x)sec^{2}(x)}{ln{10}(x)} + 49380lg(x)cos(x)cos(x)tan^{2}(x)sec^{2}(x) + 49380lg(x)sin(x)*-sin(x)tan^{2}(x)sec^{2}(x) + 49380lg(x)sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 49380lg(x)sin(x)cos(x)tan^{2}(x)*2sec^{2}(x)tan(x) - \frac{148140sin(x)cos(x)sec^{2}(x)}{ln{10}(x)} - 148140lg(x)cos(x)cos(x)sec^{2}(x) - 148140lg(x)sin(x)*-sin(x)sec^{2}(x) - 148140lg(x)sin(x)cos(x)*2sec^{2}(x)tan(x) - \frac{49380cos^{2}(x)tan(x)}{ln{10}(x)} - 49380lg(x)*-2cos(x)sin(x)tan(x) - 49380lg(x)cos^{2}(x)sec^{2}(x)(1) + \frac{49380sin^{2}(x)tan(x)}{ln{10}(x)} + 49380lg(x)*2sin(x)cos(x)tan(x) + 49380lg(x)sin^{2}(x)sec^{2}(x)(1)\\=&\frac{-148140sin(x)cos(x)tan(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{296280cos^{2}(x)tan(x)sec^{2}(x)}{xln{10}} - \frac{296280sin^{2}(x)tan(x)sec^{2}(x)}{xln{10}} + \frac{98760sin(x)cos(x)sec^{4}(x)}{xln{10}} + \frac{197520sin(x)cos(x)tan^{2}(x)sec^{2}(x)}{xln{10}} + \frac{98760cos^{2}(x)tan(x)}{x^{3}ln{10}} - \frac{148140cos^{2}(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{98760sin^{2}(x)tan(x)}{x^{3}ln{10}} + \frac{148140sin^{2}(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{98760sin(x)cos(x)sec^{2}(x)}{x^{3}ln{10}} + \frac{296280sin(x)cos(x)tan(x)}{x^{2}ln{10}} - \frac{74070sin(x)cos(x)tan(x)}{x^{4}ln{10}} - \frac{592560sin(x)cos(x)sec^{2}(x)}{xln{10}} - \frac{197520cos^{2}(x)tan(x)}{xln{10}} + \frac{197520sin^{2}(x)tan(x)}{xln{10}} + 197520lg(x)sin(x)cos(x)tan(x)sec^{4}(x) + 98760lg(x)cos^{2}(x)sec^{4}(x) + 197520lg(x)cos^{2}(x)tan^{2}(x)sec^{2}(x) - 592560lg(x)sin(x)cos(x)tan(x)sec^{2}(x) - 98760lg(x)sin^{2}(x)sec^{4}(x) - 197520lg(x)sin^{2}(x)tan^{2}(x)sec^{2}(x) + 98760lg(x)sin(x)cos(x)tan^{3}(x)sec^{2}(x) - 197520lg(x)cos^{2}(x)sec^{2}(x) + 197520lg(x)sin^{2}(x)sec^{2}(x) + 197520lg(x)sin(x)cos(x)tan(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数12345sin(x)cos(x)tan(x)lg(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 12345lg(x)sin(x)cos(x)tan(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( 12345lg(x)sin(x)cos(x)tan(x)\right)}{dx}\\=&\frac{12345sin(x)cos(x)tan(x)}{ln{10}(x)} + 12345lg(x)cos(x)cos(x)tan(x) + 12345lg(x)sin(x)*-sin(x)tan(x) + 12345lg(x)sin(x)cos(x)sec^{2}(x)(1)\\=&\frac{12345sin(x)cos(x)tan(x)}{xln{10}} + 12345lg(x)cos^{2}(x)tan(x) - 12345lg(x)sin^{2}(x)tan(x) + 12345lg(x)sin(x)cos(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{12345sin(x)cos(x)tan(x)}{xln{10}} + 12345lg(x)cos^{2}(x)tan(x) - 12345lg(x)sin^{2}(x)tan(x) + 12345lg(x)sin(x)cos(x)sec^{2}(x)\right)}{dx}\\=&\frac{12345*-sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{12345*-0sin(x)cos(x)tan(x)}{xln^{2}{10}} + \frac{12345cos(x)cos(x)tan(x)}{xln{10}} + \frac{12345sin(x)*-sin(x)tan(x)}{xln{10}} + \frac{12345sin(x)cos(x)sec^{2}(x)(1)}{xln{10}} + \frac{12345cos^{2}(x)tan(x)}{ln{10}(x)} + 12345lg(x)*-2cos(x)sin(x)tan(x) + 12345lg(x)cos^{2}(x)sec^{2}(x)(1) - \frac{12345sin^{2}(x)tan(x)}{ln{10}(x)} - 12345lg(x)*2sin(x)cos(x)tan(x) - 12345lg(x)sin^{2}(x)sec^{2}(x)(1) + \frac{12345sin(x)cos(x)sec^{2}(x)}{ln{10}(x)} + 12345lg(x)cos(x)cos(x)sec^{2}(x) + 12345lg(x)sin(x)*-sin(x)sec^{2}(x) + 12345lg(x)sin(x)cos(x)*2sec^{2}(x)tan(x)\\=&\frac{-12345sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{24690cos^{2}(x)tan(x)}{xln{10}} - \frac{24690sin^{2}(x)tan(x)}{xln{10}} + \frac{24690sin(x)cos(x)sec^{2}(x)}{xln{10}} + 24690lg(x)sin(x)cos(x)tan(x)sec^{2}(x) + 24690lg(x)cos^{2}(x)sec^{2}(x) - 49380lg(x)sin(x)cos(x)tan(x) - 24690lg(x)sin^{2}(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-12345sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{24690cos^{2}(x)tan(x)}{xln{10}} - \frac{24690sin^{2}(x)tan(x)}{xln{10}} + \frac{24690sin(x)cos(x)sec^{2}(x)}{xln{10}} + 24690lg(x)sin(x)cos(x)tan(x)sec^{2}(x) + 24690lg(x)cos^{2}(x)sec^{2}(x) - 49380lg(x)sin(x)cos(x)tan(x) - 24690lg(x)sin^{2}(x)sec^{2}(x)\right)}{dx}\\=&\frac{-12345*-2sin(x)cos(x)tan(x)}{x^{3}ln{10}} - \frac{12345*-0sin(x)cos(x)tan(x)}{x^{2}ln^{2}{10}} - \frac{12345cos(x)cos(x)tan(x)}{x^{2}ln{10}} - \frac{12345sin(x)*-sin(x)tan(x)}{x^{2}ln{10}} - \frac{12345sin(x)cos(x)sec^{2}(x)(1)}{x^{2}ln{10}} + \frac{24690*-cos^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{24690*-0cos^{2}(x)tan(x)}{xln^{2}{10}} + \frac{24690*-2cos(x)sin(x)tan(x)}{xln{10}} + \frac{24690cos^{2}(x)sec^{2}(x)(1)}{xln{10}} - \frac{24690*-sin^{2}(x)tan(x)}{x^{2}ln{10}} - \frac{24690*-0sin^{2}(x)tan(x)}{xln^{2}{10}} - \frac{24690*2sin(x)cos(x)tan(x)}{xln{10}} - \frac{24690sin^{2}(x)sec^{2}(x)(1)}{xln{10}} + \frac{24690*-sin(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{24690*-0sin(x)cos(x)sec^{2}(x)}{xln^{2}{10}} + \frac{24690cos(x)cos(x)sec^{2}(x)}{xln{10}} + \frac{24690sin(x)*-sin(x)sec^{2}(x)}{xln{10}} + \frac{24690sin(x)cos(x)*2sec^{2}(x)tan(x)}{xln{10}} + \frac{24690sin(x)cos(x)tan(x)sec^{2}(x)}{ln{10}(x)} + 24690lg(x)cos(x)cos(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)*-sin(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) + 24690lg(x)sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) + \frac{24690cos^{2}(x)sec^{2}(x)}{ln{10}(x)} + 24690lg(x)*-2cos(x)sin(x)sec^{2}(x) + 24690lg(x)cos^{2}(x)*2sec^{2}(x)tan(x) - \frac{49380sin(x)cos(x)tan(x)}{ln{10}(x)} - 49380lg(x)cos(x)cos(x)tan(x) - 49380lg(x)sin(x)*-sin(x)tan(x) - 49380lg(x)sin(x)cos(x)sec^{2}(x)(1) - \frac{24690sin^{2}(x)sec^{2}(x)}{ln{10}(x)} - 24690lg(x)*2sin(x)cos(x)sec^{2}(x) - 24690lg(x)sin^{2}(x)*2sec^{2}(x)tan(x)\\=&\frac{74070sin(x)cos(x)tan(x)sec^{2}(x)}{xln{10}} - \frac{37035cos^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{37035sin^{2}(x)tan(x)}{x^{2}ln{10}} - \frac{37035sin(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{24690sin(x)cos(x)tan(x)}{x^{3}ln{10}} + \frac{74070cos^{2}(x)sec^{2}(x)}{xln{10}} - \frac{74070sin^{2}(x)sec^{2}(x)}{xln{10}} - \frac{148140sin(x)cos(x)tan(x)}{xln{10}} + 74070lg(x)cos^{2}(x)tan(x)sec^{2}(x) - 74070lg(x)sin^{2}(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)cos(x)sec^{4}(x) + 49380lg(x)sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140lg(x)sin(x)cos(x)sec^{2}(x) - 49380lg(x)cos^{2}(x)tan(x) + 49380lg(x)sin^{2}(x)tan(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{74070sin(x)cos(x)tan(x)sec^{2}(x)}{xln{10}} - \frac{37035cos^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{37035sin^{2}(x)tan(x)}{x^{2}ln{10}} - \frac{37035sin(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{24690sin(x)cos(x)tan(x)}{x^{3}ln{10}} + \frac{74070cos^{2}(x)sec^{2}(x)}{xln{10}} - \frac{74070sin^{2}(x)sec^{2}(x)}{xln{10}} - \frac{148140sin(x)cos(x)tan(x)}{xln{10}} + 74070lg(x)cos^{2}(x)tan(x)sec^{2}(x) - 74070lg(x)sin^{2}(x)tan(x)sec^{2}(x) + 24690lg(x)sin(x)cos(x)sec^{4}(x) + 49380lg(x)sin(x)cos(x)tan^{2}(x)sec^{2}(x) - 148140lg(x)sin(x)cos(x)sec^{2}(x) - 49380lg(x)cos^{2}(x)tan(x) + 49380lg(x)sin^{2}(x)tan(x)\right)}{dx}\\=&\frac{74070*-sin(x)cos(x)tan(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{74070*-0sin(x)cos(x)tan(x)sec^{2}(x)}{xln^{2}{10}} + \frac{74070cos(x)cos(x)tan(x)sec^{2}(x)}{xln{10}} + \frac{74070sin(x)*-sin(x)tan(x)sec^{2}(x)}{xln{10}} + \frac{74070sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x)}{xln{10}} + \frac{74070sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x)}{xln{10}} - \frac{37035*-2cos^{2}(x)tan(x)}{x^{3}ln{10}} - \frac{37035*-0cos^{2}(x)tan(x)}{x^{2}ln^{2}{10}} - \frac{37035*-2cos(x)sin(x)tan(x)}{x^{2}ln{10}} - \frac{37035cos^{2}(x)sec^{2}(x)(1)}{x^{2}ln{10}} + \frac{37035*-2sin^{2}(x)tan(x)}{x^{3}ln{10}} + \frac{37035*-0sin^{2}(x)tan(x)}{x^{2}ln^{2}{10}} + \frac{37035*2sin(x)cos(x)tan(x)}{x^{2}ln{10}} + \frac{37035sin^{2}(x)sec^{2}(x)(1)}{x^{2}ln{10}} - \frac{37035*-2sin(x)cos(x)sec^{2}(x)}{x^{3}ln{10}} - \frac{37035*-0sin(x)cos(x)sec^{2}(x)}{x^{2}ln^{2}{10}} - \frac{37035cos(x)cos(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{37035sin(x)*-sin(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{37035sin(x)cos(x)*2sec^{2}(x)tan(x)}{x^{2}ln{10}} + \frac{24690*-3sin(x)cos(x)tan(x)}{x^{4}ln{10}} + \frac{24690*-0sin(x)cos(x)tan(x)}{x^{3}ln^{2}{10}} + \frac{24690cos(x)cos(x)tan(x)}{x^{3}ln{10}} + \frac{24690sin(x)*-sin(x)tan(x)}{x^{3}ln{10}} + \frac{24690sin(x)cos(x)sec^{2}(x)(1)}{x^{3}ln{10}} + \frac{74070*-cos^{2}(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{74070*-0cos^{2}(x)sec^{2}(x)}{xln^{2}{10}} + \frac{74070*-2cos(x)sin(x)sec^{2}(x)}{xln{10}} + \frac{74070cos^{2}(x)*2sec^{2}(x)tan(x)}{xln{10}} - \frac{74070*-sin^{2}(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{74070*-0sin^{2}(x)sec^{2}(x)}{xln^{2}{10}} - \frac{74070*2sin(x)cos(x)sec^{2}(x)}{xln{10}} - \frac{74070sin^{2}(x)*2sec^{2}(x)tan(x)}{xln{10}} - \frac{148140*-sin(x)cos(x)tan(x)}{x^{2}ln{10}} - \frac{148140*-0sin(x)cos(x)tan(x)}{xln^{2}{10}} - \frac{148140cos(x)cos(x)tan(x)}{xln{10}} - \frac{148140sin(x)*-sin(x)tan(x)}{xln{10}} - \frac{148140sin(x)cos(x)sec^{2}(x)(1)}{xln{10}} + \frac{74070cos^{2}(x)tan(x)sec^{2}(x)}{ln{10}(x)} + 74070lg(x)*-2cos(x)sin(x)tan(x)sec^{2}(x) + 74070lg(x)cos^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 74070lg(x)cos^{2}(x)tan(x)*2sec^{2}(x)tan(x) - \frac{74070sin^{2}(x)tan(x)sec^{2}(x)}{ln{10}(x)} - 74070lg(x)*2sin(x)cos(x)tan(x)sec^{2}(x) - 74070lg(x)sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 74070lg(x)sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) + \frac{24690sin(x)cos(x)sec^{4}(x)}{ln{10}(x)} + 24690lg(x)cos(x)cos(x)sec^{4}(x) + 24690lg(x)sin(x)*-sin(x)sec^{4}(x) + 24690lg(x)sin(x)cos(x)*4sec^{4}(x)tan(x) + \frac{49380sin(x)cos(x)tan^{2}(x)sec^{2}(x)}{ln{10}(x)} + 49380lg(x)cos(x)cos(x)tan^{2}(x)sec^{2}(x) + 49380lg(x)sin(x)*-sin(x)tan^{2}(x)sec^{2}(x) + 49380lg(x)sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 49380lg(x)sin(x)cos(x)tan^{2}(x)*2sec^{2}(x)tan(x) - \frac{148140sin(x)cos(x)sec^{2}(x)}{ln{10}(x)} - 148140lg(x)cos(x)cos(x)sec^{2}(x) - 148140lg(x)sin(x)*-sin(x)sec^{2}(x) - 148140lg(x)sin(x)cos(x)*2sec^{2}(x)tan(x) - \frac{49380cos^{2}(x)tan(x)}{ln{10}(x)} - 49380lg(x)*-2cos(x)sin(x)tan(x) - 49380lg(x)cos^{2}(x)sec^{2}(x)(1) + \frac{49380sin^{2}(x)tan(x)}{ln{10}(x)} + 49380lg(x)*2sin(x)cos(x)tan(x) + 49380lg(x)sin^{2}(x)sec^{2}(x)(1)\\=&\frac{-148140sin(x)cos(x)tan(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{296280cos^{2}(x)tan(x)sec^{2}(x)}{xln{10}} - \frac{296280sin^{2}(x)tan(x)sec^{2}(x)}{xln{10}} + \frac{98760sin(x)cos(x)sec^{4}(x)}{xln{10}} + \frac{197520sin(x)cos(x)tan^{2}(x)sec^{2}(x)}{xln{10}} + \frac{98760cos^{2}(x)tan(x)}{x^{3}ln{10}} - \frac{148140cos^{2}(x)sec^{2}(x)}{x^{2}ln{10}} - \frac{98760sin^{2}(x)tan(x)}{x^{3}ln{10}} + \frac{148140sin^{2}(x)sec^{2}(x)}{x^{2}ln{10}} + \frac{98760sin(x)cos(x)sec^{2}(x)}{x^{3}ln{10}} + \frac{296280sin(x)cos(x)tan(x)}{x^{2}ln{10}} - \frac{74070sin(x)cos(x)tan(x)}{x^{4}ln{10}} - \frac{592560sin(x)cos(x)sec^{2}(x)}{xln{10}} - \frac{197520cos^{2}(x)tan(x)}{xln{10}} + \frac{197520sin^{2}(x)tan(x)}{xln{10}} + 197520lg(x)sin(x)cos(x)tan(x)sec^{4}(x) + 98760lg(x)cos^{2}(x)sec^{4}(x) + 197520lg(x)cos^{2}(x)tan^{2}(x)sec^{2}(x) - 592560lg(x)sin(x)cos(x)tan(x)sec^{2}(x) - 98760lg(x)sin^{2}(x)sec^{4}(x) - 197520lg(x)sin^{2}(x)tan^{2}(x)sec^{2}(x) + 98760lg(x)sin(x)cos(x)tan^{3}(x)sec^{2}(x) - 197520lg(x)cos^{2}(x)sec^{2}(x) + 197520lg(x)sin^{2}(x)sec^{2}(x) + 197520lg(x)sin(x)cos(x)tan(x)\\ \end{split}\end{equation} \]
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