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 2 个题目：每一题对 x 求 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数cos(x)cos(x) - cos(cos(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = cos^{2}(x) - cos(cos(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos^{2}(x) - cos(cos(x))\right)}{dx}\\=&-2cos(x)sin(x) - -sin(cos(x))*-sin(x)\\=&-2sin(x)cos(x) - sin(x)sin(cos(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -2sin(x)cos(x) - sin(x)sin(cos(x))\right)}{dx}\\=&-2cos(x)cos(x) - 2sin(x)*-sin(x) - cos(x)sin(cos(x)) - sin(x)cos(cos(x))*-sin(x)\\=&-2cos^{2}(x) - sin(cos(x))cos(x) + sin^{2}(x)cos(cos(x)) + 2sin^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2cos^{2}(x) - sin(cos(x))cos(x) + sin^{2}(x)cos(cos(x)) + 2sin^{2}(x)\right)}{dx}\\=&-2*-2cos(x)sin(x) - cos(cos(x))*-sin(x)cos(x) - sin(cos(x))*-sin(x) + 2sin(x)cos(x)cos(cos(x)) + sin^{2}(x)*-sin(cos(x))*-sin(x) + 2*2sin(x)cos(x)\\=&2sin(x)cos(x)cos(cos(x)) + sin(x)cos(cos(x))cos(x) + sin(x)sin(cos(x)) + 8sin(x)cos(x) + sin(cos(x))sin^{3}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 2sin(x)cos(x)cos(cos(x)) + sin(x)cos(cos(x))cos(x) + sin(x)sin(cos(x)) + 8sin(x)cos(x) + sin(cos(x))sin^{3}(x)\right)}{dx}\\=&2cos(x)cos(x)cos(cos(x)) + 2sin(x)*-sin(x)cos(cos(x)) + 2sin(x)cos(x)*-sin(cos(x))*-sin(x) + cos(x)cos(cos(x))cos(x) + sin(x)*-sin(cos(x))*-sin(x)cos(x) + sin(x)cos(cos(x))*-sin(x) + cos(x)sin(cos(x)) + sin(x)cos(cos(x))*-sin(x) + 8cos(x)cos(x) + 8sin(x)*-sin(x) + cos(cos(x))*-sin(x)sin^{3}(x) + sin(cos(x))*3sin^{2}(x)cos(x)\\=&3cos^{2}(x)cos(cos(x)) - 4sin^{2}(x)cos(cos(x)) + 3sin(cos(x))sin^{2}(x)cos(x) + sin(cos(x))cos(x) + 8cos^{2}(x) + 3sin^{2}(x)sin(cos(x))cos(x) - sin^{4}(x)cos(cos(x)) - 8sin^{2}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数sin(x)sin(x) - sin(sin(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin^{2}(x) - sin(sin(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin^{2}(x) - sin(sin(x))\right)}{dx}\\=&2sin(x)cos(x) - cos(sin(x))cos(x)\\=&2sin(x)cos(x) - cos(x)cos(sin(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2sin(x)cos(x) - cos(x)cos(sin(x))\right)}{dx}\\=&2cos(x)cos(x) + 2sin(x)*-sin(x) - -sin(x)cos(sin(x)) - cos(x)*-sin(sin(x))cos(x)\\=&2cos^{2}(x) + sin(x)cos(sin(x)) + sin(sin(x))cos^{2}(x) - 2sin^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2cos^{2}(x) + sin(x)cos(sin(x)) + sin(sin(x))cos^{2}(x) - 2sin^{2}(x)\right)}{dx}\\=&2*-2cos(x)sin(x) + cos(x)cos(sin(x)) + sin(x)*-sin(sin(x))cos(x) + cos(sin(x))cos(x)cos^{2}(x) + sin(sin(x))*-2cos(x)sin(x) - 2*2sin(x)cos(x)\\=&-8sin(x)cos(x) + cos(x)cos(sin(x)) - 3sin(x)sin(sin(x))cos(x) + cos^{3}(x)cos(sin(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -8sin(x)cos(x) + cos(x)cos(sin(x)) - 3sin(x)sin(sin(x))cos(x) + cos^{3}(x)cos(sin(x))\right)}{dx}\\=&-8cos(x)cos(x) - 8sin(x)*-sin(x) + -sin(x)cos(sin(x)) + cos(x)*-sin(sin(x))cos(x) - 3cos(x)sin(sin(x))cos(x) - 3sin(x)cos(sin(x))cos(x)cos(x) - 3sin(x)sin(sin(x))*-sin(x) + -3cos^{2}(x)sin(x)cos(sin(x)) + cos^{3}(x)*-sin(sin(x))cos(x)\\=&-8cos^{2}(x) + 3sin^{2}(x)sin(sin(x)) - 6sin(x)cos^{2}(x)cos(sin(x)) - 4sin(sin(x))cos^{2}(x) - sin(x)cos(sin(x)) - sin(sin(x))cos^{4}(x) + 8sin^{2}(x)\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数cos(x)cos(x) - cos(cos(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = cos^{2}(x) - cos(cos(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos^{2}(x) - cos(cos(x))\right)}{dx}\\=&-2cos(x)sin(x) - -sin(cos(x))*-sin(x)\\=&-2sin(x)cos(x) - sin(x)sin(cos(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( -2sin(x)cos(x) - sin(x)sin(cos(x))\right)}{dx}\\=&-2cos(x)cos(x) - 2sin(x)*-sin(x) - cos(x)sin(cos(x)) - sin(x)cos(cos(x))*-sin(x)\\=&-2cos^{2}(x) - sin(cos(x))cos(x) + sin^{2}(x)cos(cos(x)) + 2sin^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -2cos^{2}(x) - sin(cos(x))cos(x) + sin^{2}(x)cos(cos(x)) + 2sin^{2}(x)\right)}{dx}\\=&-2*-2cos(x)sin(x) - cos(cos(x))*-sin(x)cos(x) - sin(cos(x))*-sin(x) + 2sin(x)cos(x)cos(cos(x)) + sin^{2}(x)*-sin(cos(x))*-sin(x) + 2*2sin(x)cos(x)\\=&2sin(x)cos(x)cos(cos(x)) + sin(x)cos(cos(x))cos(x) + sin(x)sin(cos(x)) + 8sin(x)cos(x) + sin(cos(x))sin^{3}(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( 2sin(x)cos(x)cos(cos(x)) + sin(x)cos(cos(x))cos(x) + sin(x)sin(cos(x)) + 8sin(x)cos(x) + sin(cos(x))sin^{3}(x)\right)}{dx}\\=&2cos(x)cos(x)cos(cos(x)) + 2sin(x)*-sin(x)cos(cos(x)) + 2sin(x)cos(x)*-sin(cos(x))*-sin(x) + cos(x)cos(cos(x))cos(x) + sin(x)*-sin(cos(x))*-sin(x)cos(x) + sin(x)cos(cos(x))*-sin(x) + cos(x)sin(cos(x)) + sin(x)cos(cos(x))*-sin(x) + 8cos(x)cos(x) + 8sin(x)*-sin(x) + cos(cos(x))*-sin(x)sin^{3}(x) + sin(cos(x))*3sin^{2}(x)cos(x)\\=&3cos^{2}(x)cos(cos(x)) - 4sin^{2}(x)cos(cos(x)) + 3sin(cos(x))sin^{2}(x)cos(x) + sin(cos(x))cos(x) + 8cos^{2}(x) + 3sin^{2}(x)sin(cos(x))cos(x) - sin^{4}(x)cos(cos(x)) - 8sin^{2}(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数sin(x)sin(x) - sin(sin(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sin^{2}(x) - sin(sin(x))\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin^{2}(x) - sin(sin(x))\right)}{dx}\\=&2sin(x)cos(x) - cos(sin(x))cos(x)\\=&2sin(x)cos(x) - cos(x)cos(sin(x))\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( 2sin(x)cos(x) - cos(x)cos(sin(x))\right)}{dx}\\=&2cos(x)cos(x) + 2sin(x)*-sin(x) - -sin(x)cos(sin(x)) - cos(x)*-sin(sin(x))cos(x)\\=&2cos^{2}(x) + sin(x)cos(sin(x)) + sin(sin(x))cos^{2}(x) - 2sin^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( 2cos^{2}(x) + sin(x)cos(sin(x)) + sin(sin(x))cos^{2}(x) - 2sin^{2}(x)\right)}{dx}\\=&2*-2cos(x)sin(x) + cos(x)cos(sin(x)) + sin(x)*-sin(sin(x))cos(x) + cos(sin(x))cos(x)cos^{2}(x) + sin(sin(x))*-2cos(x)sin(x) - 2*2sin(x)cos(x)\\=&-8sin(x)cos(x) + cos(x)cos(sin(x)) - 3sin(x)sin(sin(x))cos(x) + cos^{3}(x)cos(sin(x))\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -8sin(x)cos(x) + cos(x)cos(sin(x)) - 3sin(x)sin(sin(x))cos(x) + cos^{3}(x)cos(sin(x))\right)}{dx}\\=&-8cos(x)cos(x) - 8sin(x)*-sin(x) + -sin(x)cos(sin(x)) + cos(x)*-sin(sin(x))cos(x) - 3cos(x)sin(sin(x))cos(x) - 3sin(x)cos(sin(x))cos(x)cos(x) - 3sin(x)sin(sin(x))*-sin(x) + -3cos^{2}(x)sin(x)cos(sin(x)) + cos^{3}(x)*-sin(sin(x))cos(x)\\=&-8cos^{2}(x) + 3sin^{2}(x)sin(sin(x)) - 6sin(x)cos^{2}(x)cos(sin(x)) - 4sin(sin(x))cos^{2}(x) - sin(x)cos(sin(x)) - sin(sin(x))cos^{4}(x) + 8sin^{2}(x)\\ \end{split}\end{equation} \]
你的问题在这里没有得到解决？请到 热门难题 里面看看吧！
最 新 发 布
新增加身体健康评估计算器，位置：“数学运算 > 身体健康评估”。
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。