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。
\[ \begin{equation}\begin{split}【1/1】求函数{2}^{arcsin(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {2}^{arcsin(x)}\right)}{dx}\\=&({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))\\=&\frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln(2) + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x{2}^{arcsin(x)}ln(2) + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{3}{2}}(2)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{3x^{2}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3x^{2}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}{2}^{arcsin(x)}ln(2) + \frac{3*2x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{5}{2}}(2)} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}}){2}^{arcsin(x)}ln(2) + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{3}{2}}(2)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{x{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}(2)} + 2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x{2}^{arcsin(x)}ln^{2}(2) + \frac{2 * {2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{2x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{2x{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{2}(2)} + \frac{(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}}){2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)} + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*3ln^{2}(2)*0}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{15x^{3}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12x^{2}{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{3}} + \frac{3 * {2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{3x{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3x{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln^{4}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{2}^{arcsin(x)} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( {2}^{arcsin(x)}\right)}{dx}\\=&({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))\\=&\frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln(2) + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x{2}^{arcsin(x)}ln(2) + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{3}{2}}(2)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{3x^{2}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3x^{2}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}{2}^{arcsin(x)}ln(2) + \frac{3*2x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{5}{2}}(2)} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}}){2}^{arcsin(x)}ln(2) + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}*0}{(-x^{2} + 1)^{\frac{3}{2}}(2)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{x{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}(2)} + 2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})x{2}^{arcsin(x)}ln^{2}(2) + \frac{2 * {2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{2x({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{2x{2}^{arcsin(x)}*2ln(2)*0}{(-x^{2} + 1)^{2}(2)} + \frac{(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}}){2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}}){2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)} + \frac{({2}^{arcsin(x)}(((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))ln(2) + \frac{(arcsin(x))(0)}{(2)}))ln^{3}(2)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}*3ln^{2}(2)*0}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(2)}\\=&\frac{15x^{3}{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x{2}^{arcsin(x)}ln(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12x^{2}{2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{3}} + \frac{3 * {2}^{arcsin(x)}ln^{2}(2)}{(-x^{2} + 1)^{2}} + \frac{3x{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3x{2}^{arcsin(x)}ln^{3}(2)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{{2}^{arcsin(x)}ln^{4}(2)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 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。