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 4 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{arcsin(x)}^{\frac{1}{2}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arcsin^{\frac{1}{2}}(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin^{\frac{1}{2}}(x)\right)}{dx}\\=&(\frac{\frac{1}{2}(1)}{arcsin^{\frac{1}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})\\=&\frac{1}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{2arcsin^{\frac{1}{2}}(x)} + \frac{(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{x}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{x}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)}\right)}{dx}\\=&\frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x}{2arcsin^{\frac{1}{2}}(x)} + \frac{1}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{x(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{4(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{4(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{(\frac{\frac{-3}{2}(1)}{arcsin^{\frac{5}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{3x^{2}}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{1}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{x}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{x}{2(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} + \frac{3}{8(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3x^{2}}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{1}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{x}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{x}{2(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} + \frac{3}{8(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)}\right)}{dx}\\=&\frac{3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}}{2arcsin^{\frac{1}{2}}(x)} + \frac{3*2x}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{3x^{2}(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{5}{2}}} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{2arcsin^{\frac{1}{2}}(x)} + \frac{(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{4(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x}{4(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{x(\frac{\frac{-3}{2}(1)}{arcsin^{\frac{5}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x}{2arcsin^{\frac{3}{2}}(x)} - \frac{1}{2(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} - \frac{x(\frac{\frac{-3}{2}(1)}{arcsin^{\frac{5}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{2}} + \frac{3(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{8(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)} + \frac{3(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{8(-x^{2} + 1)arcsin^{\frac{5}{2}}(x)} + \frac{3(\frac{\frac{-5}{2}(1)}{arcsin^{\frac{7}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{8(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{15x^{3}}{2(-x^{2} + 1)^{\frac{7}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{9x}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{3x^{2}}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{3x^{2}}{(-x^{2} + 1)^{3}arcsin^{\frac{3}{2}}(x)} - \frac{3}{4(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} + \frac{3x}{8(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)} + \frac{3x}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{\frac{5}{2}}(x)} + \frac{9x}{8(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{5}{2}}(x)} - \frac{15}{16(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{7}{2}}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{arcsin(x)}^{\frac{1}{2}} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arcsin^{\frac{1}{2}}(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin^{\frac{1}{2}}(x)\right)}{dx}\\=&(\frac{\frac{1}{2}(1)}{arcsin^{\frac{1}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})\\=&\frac{1}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{2(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{1}{2}}(x)}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{2arcsin^{\frac{1}{2}}(x)} + \frac{(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{x}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{x}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)}\right)}{dx}\\=&\frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x}{2arcsin^{\frac{1}{2}}(x)} + \frac{1}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{x(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{4(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{4(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{(\frac{\frac{-3}{2}(1)}{arcsin^{\frac{5}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{3x^{2}}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{1}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{x}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{x}{2(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} + \frac{3}{8(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3x^{2}}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{1}{2(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{x}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{x}{2(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} + \frac{3}{8(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)}\right)}{dx}\\=&\frac{3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}}{2arcsin^{\frac{1}{2}}(x)} + \frac{3*2x}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{3x^{2}(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{5}{2}}} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{2arcsin^{\frac{1}{2}}(x)} + \frac{(\frac{\frac{-1}{2}(1)}{arcsin^{\frac{3}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{4(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x}{4(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{x(\frac{\frac{-3}{2}(1)}{arcsin^{\frac{5}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x}{2arcsin^{\frac{3}{2}}(x)} - \frac{1}{2(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} - \frac{x(\frac{\frac{-3}{2}(1)}{arcsin^{\frac{5}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{2(-x^{2} + 1)^{2}} + \frac{3(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{8(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)} + \frac{3(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{8(-x^{2} + 1)arcsin^{\frac{5}{2}}(x)} + \frac{3(\frac{\frac{-5}{2}(1)}{arcsin^{\frac{7}{2}}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{8(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{15x^{3}}{2(-x^{2} + 1)^{\frac{7}{2}}arcsin^{\frac{1}{2}}(x)} + \frac{9x}{2(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{1}{2}}(x)} - \frac{3x^{2}}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{1}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{\frac{3}{2}}(x)} - \frac{3x^{2}}{(-x^{2} + 1)^{3}arcsin^{\frac{3}{2}}(x)} - \frac{3}{4(-x^{2} + 1)^{2}arcsin^{\frac{3}{2}}(x)} + \frac{3x}{8(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{5}{2}}(x)} + \frac{3x}{4(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{\frac{5}{2}}(x)} + \frac{9x}{8(-x^{2} + 1)^{\frac{5}{2}}arcsin^{\frac{5}{2}}(x)} - \frac{15}{16(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{\frac{7}{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。