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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{x}{arcsin(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x}{arcsin(x)}\right)}{dx}\\=&\frac{1}{arcsin(x)} + x(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})\\=&\frac{1}{arcsin(x)} - \frac{x}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{arcsin(x)} - \frac{x}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)}\right)}{dx}\\=&(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})}) - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{arcsin^{2}(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)} - \frac{x(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-1}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)} - \frac{x^{2}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)} + \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)} - \frac{x^{2}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{2}(x)} + \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)}\right)}{dx}\\=&\frac{-(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{arcsin^{2}(x)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x^{2}}{arcsin^{2}(x)} - \frac{2x}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{x^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{arcsin^{2}(x)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} + \frac{2x(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-4x}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{3x^{3}}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{2x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{4x^{2}}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{2}{(-x^{2} + 1)arcsin^{3}(x)} - \frac{6x}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-4x}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{3x^{3}}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{2x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{4x^{2}}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{2}{(-x^{2} + 1)arcsin^{3}(x)} - \frac{6x}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)}\right)}{dx}\\=&\frac{-4(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x}{arcsin^{2}(x)} - \frac{4}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{4x(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} + \frac{4(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{3}}{arcsin^{2}(x)} - \frac{3*3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{3x^{3}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x^{2}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} + \frac{2*2x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{2x^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x^{2}}{arcsin^{3}(x)} + \frac{4*2x}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{4x^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}} + \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{arcsin^{3}(x)} + \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)} - \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} - \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x}{(-x^{2} + 1)arcsin^{4}(x)} - \frac{6}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} - \frac{6x(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{-21x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{4}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{8x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{24x}{(-x^{2} + 1)^{2}arcsin^{3}(x)} - \frac{12}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} - \frac{15x^{4}}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} + \frac{6x^{3}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} + \frac{24x^{3}}{(-x^{2} + 1)^{3}arcsin^{3}(x)} - \frac{6x^{2}}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} - \frac{12x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} - \frac{6}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)arcsin^{4}(x)} - \frac{18x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} - \frac{6}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)} + \frac{24x}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(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！
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。