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。
\[ \begin{equation}\begin{split}【1/1】求函数-cos(x) + 6tan(x) - 201sin(x)cos(x)tan(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( -cos(x) + 6tan(x) - 201sin(x)cos(x)tan(x)\right)}{dx}\\=&--sin(x) + 6sec^{2}(x)(1) - 201cos(x)cos(x)tan(x) - 201sin(x)*-sin(x)tan(x) - 201sin(x)cos(x)sec^{2}(x)(1)\\=&201sin^{2}(x)tan(x) + 6sec^{2}(x) - 201cos^{2}(x)tan(x) - 201sin(x)cos(x)sec^{2}(x) + sin(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 201sin^{2}(x)tan(x) + 6sec^{2}(x) - 201cos^{2}(x)tan(x) - 201sin(x)cos(x)sec^{2}(x) + sin(x)\right)}{dx}\\=&201*2sin(x)cos(x)tan(x) + 201sin^{2}(x)sec^{2}(x)(1) + 6*2sec^{2}(x)tan(x) - 201*-2cos(x)sin(x)tan(x) - 201cos^{2}(x)sec^{2}(x)(1) - 201cos(x)cos(x)sec^{2}(x) - 201sin(x)*-sin(x)sec^{2}(x) - 201sin(x)cos(x)*2sec^{2}(x)tan(x) + cos(x)\\=& - 402sin(x)cos(x)tan(x)sec^{2}(x) + 402sin^{2}(x)sec^{2}(x) + 12tan(x)sec^{2}(x) + 804sin(x)cos(x)tan(x) - 402cos^{2}(x)sec^{2}(x) + cos(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( - 402sin(x)cos(x)tan(x)sec^{2}(x) + 402sin^{2}(x)sec^{2}(x) + 12tan(x)sec^{2}(x) + 804sin(x)cos(x)tan(x) - 402cos^{2}(x)sec^{2}(x) + cos(x)\right)}{dx}\\=& - 402cos(x)cos(x)tan(x)sec^{2}(x) - 402sin(x)*-sin(x)tan(x)sec^{2}(x) - 402sin(x)cos(x)sec^{2}(x)(1)sec^{2}(x) - 402sin(x)cos(x)tan(x)*2sec^{2}(x)tan(x) + 402*2sin(x)cos(x)sec^{2}(x) + 402sin^{2}(x)*2sec^{2}(x)tan(x) + 12sec^{2}(x)(1)sec^{2}(x) + 12tan(x)*2sec^{2}(x)tan(x) + 804cos(x)cos(x)tan(x) + 804sin(x)*-sin(x)tan(x) + 804sin(x)cos(x)sec^{2}(x)(1) - 402*-2cos(x)sin(x)sec^{2}(x) - 402cos^{2}(x)*2sec^{2}(x)tan(x) + -sin(x)\\=& - 1206cos^{2}(x)tan(x)sec^{2}(x) + 1206sin^{2}(x)tan(x)sec^{2}(x) - 402sin(x)cos(x)sec^{4}(x) - 804sin(x)cos(x)tan^{2}(x)sec^{2}(x) + 2412sin(x)cos(x)sec^{2}(x) + 12sec^{4}(x) + 24tan^{2}(x)sec^{2}(x) + 804cos^{2}(x)tan(x) - 804sin^{2}(x)tan(x) - sin(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( - 1206cos^{2}(x)tan(x)sec^{2}(x) + 1206sin^{2}(x)tan(x)sec^{2}(x) - 402sin(x)cos(x)sec^{4}(x) - 804sin(x)cos(x)tan^{2}(x)sec^{2}(x) + 2412sin(x)cos(x)sec^{2}(x) + 12sec^{4}(x) + 24tan^{2}(x)sec^{2}(x) + 804cos^{2}(x)tan(x) - 804sin^{2}(x)tan(x) - sin(x)\right)}{dx}\\=& - 1206*-2cos(x)sin(x)tan(x)sec^{2}(x) - 1206cos^{2}(x)sec^{2}(x)(1)sec^{2}(x) - 1206cos^{2}(x)tan(x)*2sec^{2}(x)tan(x) + 1206*2sin(x)cos(x)tan(x)sec^{2}(x) + 1206sin^{2}(x)sec^{2}(x)(1)sec^{2}(x) + 1206sin^{2}(x)tan(x)*2sec^{2}(x)tan(x) - 402cos(x)cos(x)sec^{4}(x) - 402sin(x)*-sin(x)sec^{4}(x) - 402sin(x)cos(x)*4sec^{4}(x)tan(x) - 804cos(x)cos(x)tan^{2}(x)sec^{2}(x) - 804sin(x)*-sin(x)tan^{2}(x)sec^{2}(x) - 804sin(x)cos(x)*2tan(x)sec^{2}(x)(1)sec^{2}(x) - 804sin(x)cos(x)tan^{2}(x)*2sec^{2}(x)tan(x) + 2412cos(x)cos(x)sec^{2}(x) + 2412sin(x)*-sin(x)sec^{2}(x) + 2412sin(x)cos(x)*2sec^{2}(x)tan(x) + 12*4sec^{4}(x)tan(x) + 24*2tan(x)sec^{2}(x)(1)sec^{2}(x) + 24tan^{2}(x)*2sec^{2}(x)tan(x) + 804*-2cos(x)sin(x)tan(x) + 804cos^{2}(x)sec^{2}(x)(1) - 804*2sin(x)cos(x)tan(x) - 804sin^{2}(x)sec^{2}(x)(1) - cos(x)\\=& - 3216sin(x)cos(x)tan(x)sec^{4}(x) - 1608cos^{2}(x)sec^{4}(x) - 3216cos^{2}(x)tan^{2}(x)sec^{2}(x) + 9648sin(x)cos(x)tan(x)sec^{2}(x) + 1608sin^{2}(x)sec^{4}(x) + 3216sin^{2}(x)tan^{2}(x)sec^{2}(x) - 1608sin(x)cos(x)tan^{3}(x)sec^{2}(x) + 3216cos^{2}(x)sec^{2}(x) - 3216sin^{2}(x)sec^{2}(x) + 96tan(x)sec^{4}(x) + 48tan^{3}(x)sec^{2}(x) - 3216sin(x)cos(x)tan(x) - cos(x)\\ \end{split}\end{equation} \]
你的问题在这里没有得到解决？请到 热门难题 里面看看吧！
新增加学习笔记(安卓版)百度网盘快速下载应用程序，欢迎使用。
新增加学习笔记(安卓版)本站下载应用程序，欢迎使用。
新增线性代数行列式的计算，欢迎使用。
数学计算和一元方程已经支持正割函数和余割函数，欢迎使用。
新增加贷款计算器模块（具体位置：数学运算 > 贷款计算器），欢迎使用。