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。
\[ \begin{equation}\begin{split}【1/2】求函数sin(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(x)\right)}{dx}\\=&cos(x)\\=&cos(x)\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( cos(x)\right)}{dx}\\=&-sin(x)\\=&-sin(x)\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( -sin(x)\right)}{dx}\\=&-cos(x)\\=&-cos(x)\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( -cos(x)\right)}{dx}\\=&--sin(x)\\=&sin(x)\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数{cos(x)}^{e} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {cos(x)}^{e}\right)}{dx}\\=&({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))\\=&\frac{-{cos(x)}^{e}esin(x)}{cos(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-{cos(x)}^{e}esin(x)}{cos(x)}\right)}{dx}\\=&\frac{-({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))esin(x)}{cos(x)} - \frac{{cos(x)}^{e}*0sin(x)}{cos(x)} - \frac{{cos(x)}^{e}ecos(x)}{cos(x)} - \frac{{cos(x)}^{e}esin(x)sin(x)}{cos^{2}(x)}\\=&\frac{{cos(x)}^{e}e^{2}sin^{2}(x)}{cos^{2}(x)} - \frac{{cos(x)}^{e}esin^{2}(x)}{cos^{2}(x)} - {cos(x)}^{e}e\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{{cos(x)}^{e}e^{2}sin^{2}(x)}{cos^{2}(x)} - \frac{{cos(x)}^{e}esin^{2}(x)}{cos^{2}(x)} - {cos(x)}^{e}e\right)}{dx}\\=&\frac{({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))e^{2}sin^{2}(x)}{cos^{2}(x)} + \frac{{cos(x)}^{e}*2e*0sin^{2}(x)}{cos^{2}(x)} + \frac{{cos(x)}^{e}e^{2}*2sin(x)cos(x)}{cos^{2}(x)} + \frac{{cos(x)}^{e}e^{2}sin^{2}(x)*2sin(x)}{cos^{3}(x)} - \frac{({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))esin^{2}(x)}{cos^{2}(x)} - \frac{{cos(x)}^{e}*0sin^{2}(x)}{cos^{2}(x)} - \frac{{cos(x)}^{e}e*2sin(x)cos(x)}{cos^{2}(x)} - \frac{{cos(x)}^{e}esin^{2}(x)*2sin(x)}{cos^{3}(x)} - ({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))e - {cos(x)}^{e}*0\\=&\frac{-{cos(x)}^{e}e^{3}sin^{3}(x)}{cos^{3}(x)} + \frac{3{cos(x)}^{e}e^{2}sin(x)}{cos(x)} + \frac{3{cos(x)}^{e}e^{2}sin^{3}(x)}{cos^{3}(x)} - \frac{2{cos(x)}^{e}esin(x)}{cos(x)} - \frac{2{cos(x)}^{e}esin^{3}(x)}{cos^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-{cos(x)}^{e}e^{3}sin^{3}(x)}{cos^{3}(x)} + \frac{3{cos(x)}^{e}e^{2}sin(x)}{cos(x)} + \frac{3{cos(x)}^{e}e^{2}sin^{3}(x)}{cos^{3}(x)} - \frac{2{cos(x)}^{e}esin(x)}{cos(x)} - \frac{2{cos(x)}^{e}esin^{3}(x)}{cos^{3}(x)}\right)}{dx}\\=&\frac{-({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))e^{3}sin^{3}(x)}{cos^{3}(x)} - \frac{{cos(x)}^{e}*3e^{2}*0sin^{3}(x)}{cos^{3}(x)} - \frac{{cos(x)}^{e}e^{3}*3sin^{2}(x)cos(x)}{cos^{3}(x)} - \frac{{cos(x)}^{e}e^{3}sin^{3}(x)*3sin(x)}{cos^{4}(x)} + \frac{3({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))e^{2}sin(x)}{cos(x)} + \frac{3{cos(x)}^{e}*2e*0sin(x)}{cos(x)} + \frac{3{cos(x)}^{e}e^{2}cos(x)}{cos(x)} + \frac{3{cos(x)}^{e}e^{2}sin(x)sin(x)}{cos^{2}(x)} + \frac{3({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))e^{2}sin^{3}(x)}{cos^{3}(x)} + \frac{3{cos(x)}^{e}*2e*0sin^{3}(x)}{cos^{3}(x)} + \frac{3{cos(x)}^{e}e^{2}*3sin^{2}(x)cos(x)}{cos^{3}(x)} + \frac{3{cos(x)}^{e}e^{2}sin^{3}(x)*3sin(x)}{cos^{4}(x)} - \frac{2({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))esin(x)}{cos(x)} - \frac{2{cos(x)}^{e}*0sin(x)}{cos(x)} - \frac{2{cos(x)}^{e}ecos(x)}{cos(x)} - \frac{2{cos(x)}^{e}esin(x)sin(x)}{cos^{2}(x)} - \frac{2({cos(x)}^{e}((0)ln(cos(x)) + \frac{(e)(-sin(x))}{(cos(x))}))esin^{3}(x)}{cos^{3}(x)} - \frac{2{cos(x)}^{e}*0sin^{3}(x)}{cos^{3}(x)} - \frac{2{cos(x)}^{e}e*3sin^{2}(x)cos(x)}{cos^{3}(x)} - \frac{2{cos(x)}^{e}esin^{3}(x)*3sin(x)}{cos^{4}(x)}\\=&\frac{{cos(x)}^{e}e^{4}sin^{4}(x)}{cos^{4}(x)} - \frac{6{cos(x)}^{e}e^{3}sin^{2}(x)}{cos^{2}(x)} - \frac{6{cos(x)}^{e}e^{3}sin^{4}(x)}{cos^{4}(x)} + \frac{14{cos(x)}^{e}e^{2}sin^{2}(x)}{cos^{2}(x)} - \frac{8{cos(x)}^{e}esin^{2}(x)}{cos^{2}(x)} + \frac{11{cos(x)}^{e}e^{2}sin^{4}(x)}{cos^{4}(x)} - \frac{6{cos(x)}^{e}esin^{4}(x)}{cos^{4}(x)} + 3{cos(x)}^{e}e^{2} - 2{cos(x)}^{e}e\\ \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。