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。
\[ \begin{equation}\begin{split}【1/1】求函数log_{arcsin(x)}^{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{arcsin(x)}^{2}\right)}{dx}\\=&(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})\\=&\frac{-log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin(x)}\right)}{dx}\\=&\frac{-(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))}\\=&\frac{-xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)}\right)}{dx}\\=&\frac{-(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} - \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} - \frac{xlog_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{xlog_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))}\\=&\frac{-3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} - \frac{2log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} - \frac{2log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)}\right)}{dx}\\=&\frac{-3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}log_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{3*2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{3x^{2}(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{3x^{2}log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{3x^{2}log_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})log_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))} + \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlog_{arcsin(x)}^{2}}{ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{4log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{4x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))} - \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}*-3(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{4}(arcsin(x))(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))} - \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlog_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin^{2}(x)} + \frac{2log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} + \frac{2x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} + \frac{2xlog_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{2xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln(arcsin(x))} - \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)ln(arcsin(x))arcsin^{3}(x)} - \frac{2(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)} - \frac{2log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin^{3}(x)} - \frac{2log_{arcsin(x)}^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))}\\=&\frac{-15x^{3}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{7}{2}}ln(arcsin(x))arcsin(x)} - \frac{9xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} + \frac{3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{24x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{3}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} - \frac{10xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{8xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{12x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{3}ln(arcsin(x))arcsin^{2}(x)} + \frac{3log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} - \frac{2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)} - \frac{8xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{10xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{18xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} + \frac{24log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{4}(arcsin(x))arcsin^{4}(x)} + \frac{36log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{4}(x)} - \frac{18xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{22log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{4}(x)} - \frac{4xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{3}(x)} - \frac{6xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin^{3}(x)} + \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{4}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数log_{arcsin(x)}^{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( log_{arcsin(x)}^{2}\right)}{dx}\\=&(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})\\=&\frac{-log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin(x)}\right)}{dx}\\=&\frac{-(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))}\\=&\frac{-xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)}\right)}{dx}\\=&\frac{-(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} - \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} - \frac{xlog_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{xlog_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))}\\=&\frac{-3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} - \frac{2log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} - \frac{2log_{arcsin(x)}^{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)}\right)}{dx}\\=&\frac{-3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}log_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{3*2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{3x^{2}(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} - \frac{3x^{2}log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{3x^{2}log_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))} - \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})log_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin(x)} - \frac{(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin(x)} - \frac{log_{arcsin(x)}^{2}(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))} + \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlog_{arcsin(x)}^{2}}{ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{4log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{4x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln^{3}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{4xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))} - \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}*-3(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{4}(arcsin(x))(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))} - \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{6(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}*-2(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))(arcsin(x))arcsin^{3}(x)} - \frac{6log_{arcsin(x)}^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))} + \frac{2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlog_{arcsin(x)}^{2}}{ln(arcsin(x))arcsin^{2}(x)} + \frac{2log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} + \frac{2x(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} + \frac{2xlog_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))(arcsin(x))arcsin^{2}(x)} + \frac{2xlog_{arcsin(x)}^{2}(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln(arcsin(x))} - \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})log_{arcsin(x)}^{2}}{(-x^{2} + 1)ln(arcsin(x))arcsin^{3}(x)} - \frac{2(\frac{(\frac{(0)}{(2)} - \frac{((\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})}))log_{arcsin(x)}^{2}}{(arcsin(x))})}{(ln(arcsin(x)))})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)} - \frac{2log_{arcsin(x)}^{2}*-(\frac{(1)}{((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))(arcsin(x))arcsin^{3}(x)} - \frac{2log_{arcsin(x)}^{2}(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))}\\=&\frac{-15x^{3}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{7}{2}}ln(arcsin(x))arcsin(x)} - \frac{9xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin(x)} + \frac{3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{3x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(arcsin(x))arcsin^{2}(x)} + \frac{24x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{3}ln^{2}(arcsin(x))arcsin^{2}(x)} + \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{2}(x)} - \frac{10xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{8xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{12x^{2}log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{3}ln(arcsin(x))arcsin^{2}(x)} + \frac{3log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{2}(x)} - \frac{2xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{3}(x)} - \frac{8xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln^{3}(arcsin(x))arcsin^{3}(x)} - \frac{10xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln^{2}(arcsin(x))arcsin^{3}(x)} - \frac{18xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln^{3}(arcsin(x))arcsin^{3}(x)} + \frac{24log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{4}(arcsin(x))arcsin^{4}(x)} + \frac{36log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{3}(arcsin(x))arcsin^{4}(x)} - \frac{18xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(arcsin(x))arcsin^{3}(x)} + \frac{22log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln^{2}(arcsin(x))arcsin^{4}(x)} - \frac{4xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln(arcsin(x))arcsin^{3}(x)} - \frac{6xlog_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln(arcsin(x))arcsin^{3}(x)} + \frac{6log_{arcsin(x)}^{2}}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln(arcsin(x))arcsin^{4}(x)}\\ \end{split}\end{equation} \]
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