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 3 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{cos(x)}^{4} + ln(tan(x) + cos(x)) 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = cos^{4}(x) + ln(tan(x) + cos(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos^{4}(x) + ln(tan(x) + cos(x))\right)}{dx}\\=&-4cos^{3}(x)sin(x) + \frac{(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))}\\=&-4sin(x)cos^{3}(x) + \frac{sec^{2}(x)}{(tan(x) + cos(x))} - \frac{sin(x)}{(tan(x) + cos(x))}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -4sin(x)cos^{3}(x) + \frac{sec^{2}(x)}{(tan(x) + cos(x))} - \frac{sin(x)}{(tan(x) + cos(x))}\right)}{dx}\\=&-4cos(x)cos^{3}(x) - 4sin(x)*-3cos^{2}(x)sin(x) + (\frac{-(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))^{2}})sec^{2}(x) + \frac{2sec^{2}(x)tan(x)}{(tan(x) + cos(x))} - (\frac{-(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))^{2}})sin(x) - \frac{cos(x)}{(tan(x) + cos(x))}\\=&-4cos^{4}(x) + 12sin^{2}(x)cos^{2}(x) - \frac{sec^{4}(x)}{(tan(x) + cos(x))^{2}} + \frac{2sin(x)sec^{2}(x)}{(tan(x) + cos(x))^{2}} + \frac{2tan(x)sec^{2}(x)}{(tan(x) + cos(x))} - \frac{sin^{2}(x)}{(tan(x) + cos(x))^{2}} - \frac{cos(x)}{(tan(x) + cos(x))}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -4cos^{4}(x) + 12sin^{2}(x)cos^{2}(x) - \frac{sec^{4}(x)}{(tan(x) + cos(x))^{2}} + \frac{2sin(x)sec^{2}(x)}{(tan(x) + cos(x))^{2}} + \frac{2tan(x)sec^{2}(x)}{(tan(x) + cos(x))} - \frac{sin^{2}(x)}{(tan(x) + cos(x))^{2}} - \frac{cos(x)}{(tan(x) + cos(x))}\right)}{dx}\\=&-4*-4cos^{3}(x)sin(x) + 12*2sin(x)cos(x)cos^{2}(x) + 12sin^{2}(x)*-2cos(x)sin(x) - (\frac{-2(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))^{3}})sec^{4}(x) - \frac{4sec^{4}(x)tan(x)}{(tan(x) + cos(x))^{2}} + 2(\frac{-2(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))^{3}})sin(x)sec^{2}(x) + \frac{2cos(x)sec^{2}(x)}{(tan(x) + cos(x))^{2}} + \frac{2sin(x)*2sec^{2}(x)tan(x)}{(tan(x) + cos(x))^{2}} + 2(\frac{-(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))^{2}})tan(x)sec^{2}(x) + \frac{2sec^{2}(x)(1)sec^{2}(x)}{(tan(x) + cos(x))} + \frac{2tan(x)*2sec^{2}(x)tan(x)}{(tan(x) + cos(x))} - (\frac{-2(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))^{3}})sin^{2}(x) - \frac{2sin(x)cos(x)}{(tan(x) + cos(x))^{2}} - (\frac{-(sec^{2}(x)(1) + -sin(x))}{(tan(x) + cos(x))^{2}})cos(x) - \frac{-sin(x)}{(tan(x) + cos(x))}\\=&40sin(x)cos^{3}(x) - 24sin^{3}(x)cos(x) + \frac{2sec^{6}(x)}{(tan(x) + cos(x))^{3}} - \frac{6sin(x)sec^{4}(x)}{(tan(x) + cos(x))^{3}} - \frac{6tan(x)sec^{4}(x)}{(tan(x) + cos(x))^{2}} + \frac{6sin^{2}(x)sec^{2}(x)}{(tan(x) + cos(x))^{3}} + \frac{3cos(x)sec^{2}(x)}{(tan(x) + cos(x))^{2}} + \frac{6sin(x)tan(x)sec^{2}(x)}{(tan(x) + cos(x))^{2}} + \frac{2sec^{4}(x)}{(tan(x) + cos(x))} + \frac{4tan^{2}(x)sec^{2}(x)}{(tan(x) + cos(x))} - \frac{3sin(x)cos(x)}{(tan(x) + cos(x))^{2}} - \frac{2sin^{3}(x)}{(tan(x) + cos(x))^{3}} + \frac{sin(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。