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。
\[ \begin{equation}\begin{split}【1/1】求函数{arcsin(x)}^{23456789} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arcsin^{23456789}(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin^{23456789}(x)\right)}{dx}\\=&(\frac{23456789arcsin^{23456788}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})\\=&\frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&23456789(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456788}(x) + \frac{23456789(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{23456789xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-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{23456789xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&23456789(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin^{23456788}(x) + \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{23456789x(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{550220926733732(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{550220926733732(\frac{23456787arcsin^{23456786}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{70370367x^{2}arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{1100441853467464xarcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116arcsin^{23456786}(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{70370367x^{2}arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{1100441853467464xarcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116arcsin^{23456786}(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&70370367(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}arcsin^{23456788}(x) + \frac{70370367*2xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{70370367x^{2}(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} + 23456789(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})arcsin^{23456788}(x) + \frac{23456789(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732x(\frac{23456787arcsin^{23456786}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + 1100441853467464(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xarcsin^{23456787}(x) + \frac{1100441853467464arcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} + \frac{1100441853467464x(\frac{23456787arcsin^{23456786}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})arcsin^{23456786}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{6305770260928892116(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456786}(x)}{(-x^{2} + 1)} - \frac{6305770260928892116(\frac{23456786arcsin^{23456785}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{351851835x^{3}arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{211111101xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{1650662780201196x^{2}arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{6602651120804784x^{2}arcsin^{23456787}(x)}{(-x^{2} + 1)^{3}} + \frac{1650662780201196arcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116xarcsin^{23456786}(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{5835203551851767384xarcsin^{23456786}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}} - \frac{470566709077124732xarcsin^{23456786}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{7596301620547639016arcsin^{23456785}(x)}{(-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。
\[ \begin{equation}\begin{split}【1/1】求函数{arcsin(x)}^{23456789} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arcsin^{23456789}(x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin^{23456789}(x)\right)}{dx}\\=&(\frac{23456789arcsin^{23456788}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})\\=&\frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&23456789(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456788}(x) + \frac{23456789(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{23456789xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-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{23456789xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&23456789(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin^{23456788}(x) + \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{23456789x(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{550220926733732(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{550220926733732(\frac{23456787arcsin^{23456786}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{70370367x^{2}arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{1100441853467464xarcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116arcsin^{23456786}(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{70370367x^{2}arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{23456789arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{1100441853467464xarcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116arcsin^{23456786}(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&70370367(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}arcsin^{23456788}(x) + \frac{70370367*2xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{70370367x^{2}(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} + 23456789(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})arcsin^{23456788}(x) + \frac{23456789(\frac{23456788arcsin^{23456787}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{550220926733732x(\frac{23456787arcsin^{23456786}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + 1100441853467464(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xarcsin^{23456787}(x) + \frac{1100441853467464arcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} + \frac{1100441853467464x(\frac{23456787arcsin^{23456786}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})arcsin^{23456786}(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{6305770260928892116(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin^{23456786}(x)}{(-x^{2} + 1)} - \frac{6305770260928892116(\frac{23456786arcsin^{23456785}(x)(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{351851835x^{3}arcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{211111101xarcsin^{23456788}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{1650662780201196x^{2}arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}} + \frac{550220926733732arcsin^{23456787}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} + \frac{6602651120804784x^{2}arcsin^{23456787}(x)}{(-x^{2} + 1)^{3}} + \frac{1650662780201196arcsin^{23456787}(x)}{(-x^{2} + 1)^{2}} - \frac{6305770260928892116xarcsin^{23456786}(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{5835203551851767384xarcsin^{23456786}(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}} - \frac{470566709077124732xarcsin^{23456786}(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{7596301620547639016arcsin^{23456785}(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]
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