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。
\[ \begin{equation}\begin{split}【1/1】求函数arcsin(x)arccos(x)arctan(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin(x)arccos(x)arctan(x)\right)}{dx}\\=&(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)arctan(x) + arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x) + arcsin(x)arccos(x)(\frac{(1)}{(1 + (x)^{2})})\\=&\frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arcsin(x)arccos(x)}{(x^{2} + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arcsin(x)arccos(x)}{(x^{2} + 1)}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arccos(x)arctan(x) + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin(x)arctan(x) - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}} + (\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arcsin(x)arccos(x) + \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)} + \frac{arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)}\\=&\frac{xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2xarcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2xarcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarccos(x)arctan(x) + \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{xarccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arccos(x)}{(x^{2} + 1)} + \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin(x)arctan(x) - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{xarcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin(x)}{(x^{2} + 1)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)arccos(x) - \frac{2arcsin(x)arccos(x)}{(x^{2} + 1)^{2}} - \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)^{2}} - \frac{2xarcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arccos(x)}{(x^{2} + 1)} + \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin(x)}{(x^{2} + 1)} - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{3x^{2}arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3xarccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{4xarctan(x)}{(-x^{2} + 1)^{2}} - \frac{4xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{8x^{2}arcsin(x)arccos(x)}{(x^{2} + 1)^{3}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3x^{2}arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2arcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{1}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{xarcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2}{(-x^{2} + 1)(x^{2} + 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3x^{2}arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3xarccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{4xarctan(x)}{(-x^{2} + 1)^{2}} - \frac{4xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{8x^{2}arcsin(x)arccos(x)}{(x^{2} + 1)^{3}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3x^{2}arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2arcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{1}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{xarcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2}{(-x^{2} + 1)(x^{2} + 1)}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}arccos(x)arctan(x) + \frac{3*2xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}arccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})arccos(x)arctan(x) + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{arccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{x(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarccos(x)}{(x^{2} + 1)} + \frac{3(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})xarccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{3arccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{3x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - 4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xarctan(x) - \frac{4arctan(x)}{(-x^{2} + 1)^{2}} - \frac{4x(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{2}} - \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarccos(x)}{(x^{2} + 1)^{2}} - \frac{4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{4arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{4x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + 8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2}arcsin(x)arccos(x) + \frac{8*2xarcsin(x)arccos(x)}{(x^{2} + 1)^{3}} + \frac{8x^{2}(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)^{3}} + \frac{8x^{2}arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{3}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - 3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}arcsin(x)arctan(x) - \frac{3*2xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{3x^{2}(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{3x^{2}arcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{5}{2}}} - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})arcsin(x)arctan(x) - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin(x)}{(x^{2} + 1)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin(x)}{(x^{2} + 1)^{2}} + \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarccos(x)}{(x^{2} + 1)^{2}} - \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin(x)}{(x^{2} + 1)^{2}} + \frac{2arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})arcsin(x)arccos(x) - \frac{2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)^{2}} - \frac{2arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}} + \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin(x)}{(x^{2} + 1)^{2}} + \frac{2arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin(x)}{(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{(x^{2} + 1)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)}\\=&\frac{15x^{3}arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{3x^{2}arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{5}{2}}(x^{2} + 1)} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{4arccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{24x^{2}arctan(x)}{(-x^{2} + 1)^{3}} - \frac{6arctan(x)}{(-x^{2} + 1)^{2}} - \frac{12x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)^{2}} + \frac{24xarcsin(x)arccos(x)}{(x^{2} + 1)^{3}} + \frac{6x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)^{2}} + \frac{8x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} + \frac{24x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{6arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{48x^{3}arcsin(x)arccos(x)}{(x^{2} + 1)^{4}} - \frac{8x^{2}arcsin(x)}{(x^{2} + 1)^{3}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6x^{2}arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3x^{2}arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}} - \frac{8x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{15x^{3}arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{7}{2}}} - \frac{9xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{9x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{5}{2}}(x^{2} + 1)} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{3x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{2x}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{16x^{2}arcsin(x)}{(x^{2} + 1)^{3}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2x}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{3x^{2}arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{5}{2}}} + \frac{4arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{4x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{8x}{(x^{2} + 1)^{2}(-x^{2} + 1)} - \frac{x}{(x^{2} + 1)(-x^{2} + 1)^{2}} - \frac{17x}{(-x^{2} + 1)^{2}(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} + \frac{4x}{(-x^{2} + 1)(x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数arcsin(x)arccos(x)arctan(x) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arcsin(x)arccos(x)arctan(x)\right)}{dx}\\=&(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)arctan(x) + arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x) + arcsin(x)arccos(x)(\frac{(1)}{(1 + (x)^{2})})\\=&\frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arcsin(x)arccos(x)}{(x^{2} + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arcsin(x)arccos(x)}{(x^{2} + 1)}\right)}{dx}\\=&(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arccos(x)arctan(x) + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}} - (\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin(x)arctan(x) - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}} + (\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arcsin(x)arccos(x) + \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)} + \frac{arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)}\\=&\frac{xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2xarcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2xarcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarccos(x)arctan(x) + \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{xarccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arccos(x)}{(x^{2} + 1)} + \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin(x)arctan(x) - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{xarcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin(x)}{(x^{2} + 1)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)arccos(x) - \frac{2arcsin(x)arccos(x)}{(x^{2} + 1)^{2}} - \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)^{2}} - \frac{2xarcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arccos(x)}{(x^{2} + 1)} + \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})arcsin(x)}{(x^{2} + 1)} - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}}\\=&\frac{3x^{2}arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3xarccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{4xarctan(x)}{(-x^{2} + 1)^{2}} - \frac{4xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{8x^{2}arcsin(x)arccos(x)}{(x^{2} + 1)^{3}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3x^{2}arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2arcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{1}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{xarcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2}{(-x^{2} + 1)(x^{2} + 1)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{3x^{2}arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3xarccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{4xarctan(x)}{(-x^{2} + 1)^{2}} - \frac{4xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{8x^{2}arcsin(x)arccos(x)}{(x^{2} + 1)^{3}} - \frac{xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3x^{2}arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{2xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2arcsin(x)arccos(x)}{(x^{2} + 1)^{2}} + \frac{2xarcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{1}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{xarcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2}{(-x^{2} + 1)(x^{2} + 1)}\right)}{dx}\\=&3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}arccos(x)arctan(x) + \frac{3*2xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{3x^{2}arccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{5}{2}}} + (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})arccos(x)arctan(x) + \frac{(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{arccos(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{x(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarccos(x)}{(x^{2} + 1)} + \frac{3(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})xarccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{3arccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{3x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - 4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xarctan(x) - \frac{4arctan(x)}{(-x^{2} + 1)^{2}} - \frac{4x(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{2}} - \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarccos(x)}{(x^{2} + 1)^{2}} - \frac{4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{4arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{4x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + 8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2}arcsin(x)arccos(x) + \frac{8*2xarcsin(x)arccos(x)}{(x^{2} + 1)^{3}} + \frac{8x^{2}(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)^{3}} + \frac{8x^{2}arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{3}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - 3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}arcsin(x)arctan(x) - \frac{3*2xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{3x^{2}(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{3x^{2}arcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{5}{2}}} - (\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})arcsin(x)arctan(x) - \frac{(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{arcsin(x)(\frac{(1)}{(1 + (x)^{2})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin(x)}{(x^{2} + 1)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin(x)}{(x^{2} + 1)^{2}} + \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarccos(x)}{(x^{2} + 1)^{2}} - \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2x(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin(x)}{(x^{2} + 1)^{2}} + \frac{2arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})arcsin(x)arccos(x) - \frac{2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})arccos(x)}{(x^{2} + 1)^{2}} - \frac{2arcsin(x)(\frac{-(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}} + \frac{2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xarcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xarcsin(x)}{(x^{2} + 1)^{2}} + \frac{2arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})xarcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xarcsin(x)}{(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} - \frac{(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{(x^{2} + 1)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(-x^{2} + 1)}\\=&\frac{15x^{3}arccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9xarccos(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{3x^{2}arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{5}{2}}(x^{2} + 1)} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{4arccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{24x^{2}arctan(x)}{(-x^{2} + 1)^{3}} - \frac{6arctan(x)}{(-x^{2} + 1)^{2}} - \frac{12x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)^{2}} + \frac{24xarcsin(x)arccos(x)}{(x^{2} + 1)^{3}} + \frac{6x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)^{2}} + \frac{8x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} + \frac{24x^{2}arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{6arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{48x^{3}arcsin(x)arccos(x)}{(x^{2} + 1)^{4}} - \frac{8x^{2}arcsin(x)}{(x^{2} + 1)^{3}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6x^{2}arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3x^{2}arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}} - \frac{8x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{15x^{3}arcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{7}{2}}} - \frac{9xarcsin(x)arctan(x)}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{9x^{2}arcsin(x)}{(-x^{2} + 1)^{\frac{5}{2}}(x^{2} + 1)} - \frac{arctan(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{3arcsin(x)}{(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{3x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}(x^{2} + 1)} - \frac{2x}{(x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}} - \frac{16x^{2}arcsin(x)}{(x^{2} + 1)^{3}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2arcsin(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2x}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{3x^{2}arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{5}{2}}} + \frac{4arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{4x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2arccos(x)}{(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2arcsin(x)}{(x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{8x}{(x^{2} + 1)^{2}(-x^{2} + 1)} - \frac{x}{(x^{2} + 1)(-x^{2} + 1)^{2}} - \frac{17x}{(-x^{2} + 1)^{2}(x^{2} + 1)} - \frac{arcsin(x)}{(x^{2} + 1)(-x^{2} + 1)^{\frac{3}{2}}} - \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}(x^{2} + 1)} + \frac{4x}{(-x^{2} + 1)(x^{2} + 1)^{2}}\\ \end{split}\end{equation} \]
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