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。
\[ \begin{equation}\begin{split}【1/2】求函数sin(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(lg(x))\right)}{dx}\\=&\frac{cos(lg(x))}{ln{10}(x)}\\=&\frac{cos(lg(x))}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cos(lg(x))}{xln{10}}\right)}{dx}\\=&\frac{-cos(lg(x))}{x^{2}ln{10}} + \frac{-0cos(lg(x))}{xln^{2}{10}} + \frac{-sin(lg(x))}{xln{10}ln{10}(x)}\\=&\frac{-cos(lg(x))}{x^{2}ln{10}} - \frac{sin(lg(x))}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-cos(lg(x))}{x^{2}ln{10}} - \frac{sin(lg(x))}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{--2cos(lg(x))}{x^{3}ln{10}} - \frac{-0cos(lg(x))}{x^{2}ln^{2}{10}} - \frac{-sin(lg(x))}{x^{2}ln{10}ln{10}(x)} - \frac{-2sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{-2*0sin(lg(x))}{x^{2}ln^{3}{10}} - \frac{cos(lg(x))}{x^{2}ln^{2}{10}ln{10}(x)}\\=&\frac{2cos(lg(x))}{x^{3}ln{10}} + \frac{3sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(lg(x))}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2cos(lg(x))}{x^{3}ln{10}} + \frac{3sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(lg(x))}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{2*-3cos(lg(x))}{x^{4}ln{10}} + \frac{2*-0cos(lg(x))}{x^{3}ln^{2}{10}} + \frac{2*-sin(lg(x))}{x^{3}ln{10}ln{10}(x)} + \frac{3*-3sin(lg(x))}{x^{4}ln^{2}{10}} + \frac{3*-2*0sin(lg(x))}{x^{3}ln^{3}{10}} + \frac{3cos(lg(x))}{x^{3}ln^{2}{10}ln{10}(x)} - \frac{-3cos(lg(x))}{x^{4}ln^{3}{10}} - \frac{-3*0cos(lg(x))}{x^{3}ln^{4}{10}} - \frac{-sin(lg(x))}{x^{3}ln^{3}{10}ln{10}(x)}\\=&\frac{-6cos(lg(x))}{x^{4}ln{10}} - \frac{11sin(lg(x))}{x^{4}ln^{2}{10}} + \frac{6cos(lg(x))}{x^{4}ln^{3}{10}} + \frac{sin(lg(x))}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数cos(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(lg(x))\right)}{dx}\\=&\frac{-sin(lg(x))}{ln{10}(x)}\\=&\frac{-sin(lg(x))}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(lg(x))}{xln{10}}\right)}{dx}\\=&\frac{--sin(lg(x))}{x^{2}ln{10}} - \frac{-0sin(lg(x))}{xln^{2}{10}} - \frac{cos(lg(x))}{xln{10}ln{10}(x)}\\=&\frac{sin(lg(x))}{x^{2}ln{10}} - \frac{cos(lg(x))}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sin(lg(x))}{x^{2}ln{10}} - \frac{cos(lg(x))}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{-2sin(lg(x))}{x^{3}ln{10}} + \frac{-0sin(lg(x))}{x^{2}ln^{2}{10}} + \frac{cos(lg(x))}{x^{2}ln{10}ln{10}(x)} - \frac{-2cos(lg(x))}{x^{3}ln^{2}{10}} - \frac{-2*0cos(lg(x))}{x^{2}ln^{3}{10}} - \frac{-sin(lg(x))}{x^{2}ln^{2}{10}ln{10}(x)}\\=&\frac{-2sin(lg(x))}{x^{3}ln{10}} + \frac{3cos(lg(x))}{x^{3}ln^{2}{10}} + \frac{sin(lg(x))}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-2sin(lg(x))}{x^{3}ln{10}} + \frac{3cos(lg(x))}{x^{3}ln^{2}{10}} + \frac{sin(lg(x))}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{-2*-3sin(lg(x))}{x^{4}ln{10}} - \frac{2*-0sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{2cos(lg(x))}{x^{3}ln{10}ln{10}(x)} + \frac{3*-3cos(lg(x))}{x^{4}ln^{2}{10}} + \frac{3*-2*0cos(lg(x))}{x^{3}ln^{3}{10}} + \frac{3*-sin(lg(x))}{x^{3}ln^{2}{10}ln{10}(x)} + \frac{-3sin(lg(x))}{x^{4}ln^{3}{10}} + \frac{-3*0sin(lg(x))}{x^{3}ln^{4}{10}} + \frac{cos(lg(x))}{x^{3}ln^{3}{10}ln{10}(x)}\\=&\frac{6sin(lg(x))}{x^{4}ln{10}} - \frac{11cos(lg(x))}{x^{4}ln^{2}{10}} - \frac{6sin(lg(x))}{x^{4}ln^{3}{10}} + \frac{cos(lg(x))}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/2】求函数sin(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sin(lg(x))\right)}{dx}\\=&\frac{cos(lg(x))}{ln{10}(x)}\\=&\frac{cos(lg(x))}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{cos(lg(x))}{xln{10}}\right)}{dx}\\=&\frac{-cos(lg(x))}{x^{2}ln{10}} + \frac{-0cos(lg(x))}{xln^{2}{10}} + \frac{-sin(lg(x))}{xln{10}ln{10}(x)}\\=&\frac{-cos(lg(x))}{x^{2}ln{10}} - \frac{sin(lg(x))}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-cos(lg(x))}{x^{2}ln{10}} - \frac{sin(lg(x))}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{--2cos(lg(x))}{x^{3}ln{10}} - \frac{-0cos(lg(x))}{x^{2}ln^{2}{10}} - \frac{-sin(lg(x))}{x^{2}ln{10}ln{10}(x)} - \frac{-2sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{-2*0sin(lg(x))}{x^{2}ln^{3}{10}} - \frac{cos(lg(x))}{x^{2}ln^{2}{10}ln{10}(x)}\\=&\frac{2cos(lg(x))}{x^{3}ln{10}} + \frac{3sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(lg(x))}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2cos(lg(x))}{x^{3}ln{10}} + \frac{3sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{cos(lg(x))}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{2*-3cos(lg(x))}{x^{4}ln{10}} + \frac{2*-0cos(lg(x))}{x^{3}ln^{2}{10}} + \frac{2*-sin(lg(x))}{x^{3}ln{10}ln{10}(x)} + \frac{3*-3sin(lg(x))}{x^{4}ln^{2}{10}} + \frac{3*-2*0sin(lg(x))}{x^{3}ln^{3}{10}} + \frac{3cos(lg(x))}{x^{3}ln^{2}{10}ln{10}(x)} - \frac{-3cos(lg(x))}{x^{4}ln^{3}{10}} - \frac{-3*0cos(lg(x))}{x^{3}ln^{4}{10}} - \frac{-sin(lg(x))}{x^{3}ln^{3}{10}ln{10}(x)}\\=&\frac{-6cos(lg(x))}{x^{4}ln{10}} - \frac{11sin(lg(x))}{x^{4}ln^{2}{10}} + \frac{6cos(lg(x))}{x^{4}ln^{3}{10}} + \frac{sin(lg(x))}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
\[ \begin{equation}\begin{split}【2/2】求函数cos(lg(x)) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( cos(lg(x))\right)}{dx}\\=&\frac{-sin(lg(x))}{ln{10}(x)}\\=&\frac{-sin(lg(x))}{xln{10}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-sin(lg(x))}{xln{10}}\right)}{dx}\\=&\frac{--sin(lg(x))}{x^{2}ln{10}} - \frac{-0sin(lg(x))}{xln^{2}{10}} - \frac{cos(lg(x))}{xln{10}ln{10}(x)}\\=&\frac{sin(lg(x))}{x^{2}ln{10}} - \frac{cos(lg(x))}{x^{2}ln^{2}{10}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sin(lg(x))}{x^{2}ln{10}} - \frac{cos(lg(x))}{x^{2}ln^{2}{10}}\right)}{dx}\\=&\frac{-2sin(lg(x))}{x^{3}ln{10}} + \frac{-0sin(lg(x))}{x^{2}ln^{2}{10}} + \frac{cos(lg(x))}{x^{2}ln{10}ln{10}(x)} - \frac{-2cos(lg(x))}{x^{3}ln^{2}{10}} - \frac{-2*0cos(lg(x))}{x^{2}ln^{3}{10}} - \frac{-sin(lg(x))}{x^{2}ln^{2}{10}ln{10}(x)}\\=&\frac{-2sin(lg(x))}{x^{3}ln{10}} + \frac{3cos(lg(x))}{x^{3}ln^{2}{10}} + \frac{sin(lg(x))}{x^{3}ln^{3}{10}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-2sin(lg(x))}{x^{3}ln{10}} + \frac{3cos(lg(x))}{x^{3}ln^{2}{10}} + \frac{sin(lg(x))}{x^{3}ln^{3}{10}}\right)}{dx}\\=&\frac{-2*-3sin(lg(x))}{x^{4}ln{10}} - \frac{2*-0sin(lg(x))}{x^{3}ln^{2}{10}} - \frac{2cos(lg(x))}{x^{3}ln{10}ln{10}(x)} + \frac{3*-3cos(lg(x))}{x^{4}ln^{2}{10}} + \frac{3*-2*0cos(lg(x))}{x^{3}ln^{3}{10}} + \frac{3*-sin(lg(x))}{x^{3}ln^{2}{10}ln{10}(x)} + \frac{-3sin(lg(x))}{x^{4}ln^{3}{10}} + \frac{-3*0sin(lg(x))}{x^{3}ln^{4}{10}} + \frac{cos(lg(x))}{x^{3}ln^{3}{10}ln{10}(x)}\\=&\frac{6sin(lg(x))}{x^{4}ln{10}} - \frac{11cos(lg(x))}{x^{4}ln^{2}{10}} - \frac{6sin(lg(x))}{x^{4}ln^{3}{10}} + \frac{cos(lg(x))}{x^{4}ln^{4}{10}}\\ \end{split}\end{equation} \]
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。