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 2 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt(1 + \frac{0.69675{x}^{2}}{({x}^{2} - {0.069066}^{2})}) 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(\frac{0.69675x}{(x - 0.069066)} + 1)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(\frac{0.69675x}{(x - 0.069066)} + 1)\right)}{dx}\\=&\frac{(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)*0.5}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\=&\frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{-0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}})x}{(x - 0.069066)(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}})}{(x - 0.069066)}\\=&\frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.121365140625x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.121365140625x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt(1 + \frac{0.69675{x}^{2}}{({x}^{2} - {0.069066}^{2})}) 关于 x 的 2 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(\frac{0.69675x}{(x - 0.069066)} + 1)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(\frac{0.69675x}{(x - 0.069066)} + 1)\right)}{dx}\\=&\frac{(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)*0.5}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\=&\frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-0.348375x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{-0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.348375(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}})x}{(x - 0.069066)(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375(\frac{-(1 + 0)}{(x - 0.069066)^{2}})}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375(\frac{-0.5(0.69675(\frac{-(1 + 0)}{(x - 0.069066)^{2}})x + \frac{0.69675}{(x - 0.069066)} + 0)}{(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}})}{(x - 0.069066)}\\=&\frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} + \frac{0.348375x}{(x - 0.069066)(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625x^{2}}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} + \frac{0.121365140625x}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)} + \frac{0.121365140625x}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}} - \frac{0.121365140625}{(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{3}{2}}(x - 0.069066)} - \frac{0.348375}{(x - 0.069066)(x - 0.069066)(\frac{0.69675x}{(x - 0.069066)} + 1)^{\frac{1}{2}}}\\ \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。