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。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{lg(x)}{sqrt(1 - xx)} - \frac{arcsin(x)}{(ln(10)x)}){\frac{1}{arcsin(x)}}^{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{lg(x)}{arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{1}{xln(10)arcsin(x)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{lg(x)}{arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{1}{xln(10)arcsin(x)}\right)}{dx}\\=&\frac{1}{ln{10}(x)arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{sqrt(-x^{2} + 1)} + \frac{lg(x)*-(-2x + 0)*\frac{1}{2}}{arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{-1}{x^{2}ln(10)arcsin(x)} - \frac{-0}{xln^{2}(10)(10)arcsin(x)} - \frac{(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{xln(10)}\\=&\frac{1}{xln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{1}{x^{2}ln(10)arcsin(x)} + \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{2}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{1}{x^{2}ln(10)arcsin(x)} + \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{2}(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{-0}{xln^{2}{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{xln{10}sqrt(-x^{2} + 1)} + \frac{-(-2x + 0)*\frac{1}{2}}{xln{10}arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}sqrt(-x^{2} + 1)} - \frac{2lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{arcsin^{2}(x)} + \frac{lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{xlg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{-2}{x^{3}ln(10)arcsin(x)} + \frac{-0}{x^{2}ln^{2}(10)(10)arcsin(x)} + \frac{(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{2}ln(10)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{xln(10)arcsin^{2}(x)} + \frac{-1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} + \frac{-0}{(-x^{2} + 1)^{\frac{1}{2}}xln^{2}(10)(10)arcsin^{2}(x)} + \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)}\\=&\frac{-1}{x^{2}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{2xlg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{3x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2}{x^{3}ln(10)arcsin(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{2}(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{2xlg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{3x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2}{x^{3}ln(10)arcsin(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{2}(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{-0}{x^{2}ln^{2}{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{2}ln{10}sqrt(-x^{2} + 1)} - \frac{-(-2x + 0)*\frac{1}{2}}{x^{2}ln{10}arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}xln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}sqrt(-x^{2} + 1)} - \frac{2*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{ln{10}arcsin^{2}(x)} + \frac{2*-0}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}{10}arcsin^{2}(x)} + \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2x}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2xlg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} - \frac{2xlg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}xln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}sqrt(-x^{2} + 1)} - \frac{2*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}sqrt(-x^{2} + 1)} + \frac{6lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} - \frac{2x}{(-x^{2} + 1)^{2}ln{10}(x)arcsin^{3}(x)} - \frac{2xlg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}} + \frac{3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}lg(x)}{arcsin^{2}(x)} + \frac{3*2xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{3x^{2}lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})lg(x)}{arcsin^{2}(x)} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)} - \frac{2xlg(x)(\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{2*-3}{x^{4}ln(10)arcsin(x)} - \frac{2*-0}{x^{3}ln^{2}(10)(10)arcsin(x)} - \frac{2(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{3}ln(10)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln(10)arcsin^{2}(x)} - \frac{-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}(10)(10)arcsin^{2}(x)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{ln(10)arcsin^{2}(x)} + \frac{-0}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln(10)arcsin^{2}(x)} - \frac{-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}(10)(10)arcsin^{2}(x)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln^{2}(10)(10)arcsin^{3}(x)} - \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)}\\=&\frac{2}{x^{3}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{8}{(-x^{2} + 1)^{2}ln{10}arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} - \frac{24lg(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} - \frac{4lg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{15x^{3}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} + \frac{9xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6}{x^{4}ln(10)arcsin(x)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}xln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{3x}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{3}(x)} - \frac{4}{(-x^{2} + 1)^{2}ln(10)arcsin^{3}(x)} + \frac{2}{(-x^{2} + 1)x^{2}ln(10)arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{4}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{8}{(-x^{2} + 1)^{2}ln{10}arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} - \frac{24lg(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} - \frac{4lg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{15x^{3}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} + \frac{9xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6}{x^{4}ln(10)arcsin(x)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}xln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{3x}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{3}(x)} - \frac{4}{(-x^{2} + 1)^{2}ln(10)arcsin^{3}(x)} + \frac{2}{(-x^{2} + 1)x^{2}ln(10)arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{4}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2*-0}{x^{3}ln^{2}{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{3}ln{10}sqrt(-x^{2} + 1)} + \frac{2*-(-2x + 0)*\frac{1}{2}}{x^{3}ln{10}arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2*-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}sqrt(-x^{2} + 1)} + \frac{2*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{6(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6*-0}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}sqrt(-x^{2} + 1)} - \frac{6*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4*-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}sqrt(-x^{2} + 1)} + \frac{4*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12*-1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln^{2}{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}sqrt(-x^{2} + 1)} + \frac{12*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{8(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})}{ln{10}arcsin^{3}(x)} - \frac{8*-0}{(-x^{2} + 1)^{2}ln^{2}{10}arcsin^{3}(x)} - \frac{8(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln{10}} + \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6*-1}{(-x^{2} + 1)x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6*-0}{(-x^{2} + 1)xln^{2}{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)xln{10}sqrt(-x^{2} + 1)} + \frac{6*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)xln{10}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)} - \frac{4(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}ln{10}arcsin^{3}(x)} - \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}{10}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{3}{2}}ln{10}} - \frac{6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}lg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6*2xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6x^{2}lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}sqrt(-x^{2} + 1)} - \frac{6x^{2}lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})lg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} - \frac{2lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} + \frac{6xlg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12lg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12x}{(-x^{2} + 1)^{2}ln{10}(x)arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}sqrt(-x^{2} + 1)} + \frac{12xlg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{2}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{18(\frac{-3(-2x + 0)}{(-x^{2} + 1)^{4}})x^{2}lg(x)}{arcsin^{3}(x)} - \frac{18*2xlg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} - \frac{18x^{2}}{(-x^{2} + 1)^{3}ln{10}(x)arcsin^{3}(x)} - \frac{18x^{2}lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{3}} + \frac{9(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x}{ln{10}arcsin^{2}(x)} + \frac{9}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} + \frac{9x*-0}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}{10}arcsin^{2}(x)} + \frac{9x(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}} - \frac{24(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{24(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{24}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{24lg(x)(\frac{-5(1)}{arcsin^{6}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}sqrt(-x^{2} + 1)} - \frac{24lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})xlg(x)}{arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} + \frac{6x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{4}(x)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})lg(x)}{arcsin^{3}(x)} - \frac{4}{(-x^{2} + 1)^{2}ln{10}(x)arcsin^{3}(x)} - \frac{4lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{6(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln{10}(x)arcsin^{4}(x)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}} + \frac{15(\frac{\frac{-7}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{9}{2}}})x^{3}lg(x)}{arcsin^{2}(x)} + \frac{15*3x^{2}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} + \frac{15x^{3}}{(-x^{2} + 1)^{\frac{7}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{15x^{3}lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})xlg(x)}{arcsin^{2}(x)} + \frac{9lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{9xlg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{6*2xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{6x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{3}(x)} - \frac{6x^{2}lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)} - \frac{2lg(x)(\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{6(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6x}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{4}(x)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6*-4}{x^{5}ln(10)arcsin(x)} + \frac{6*-0}{x^{4}ln^{2}(10)(10)arcsin(x)} + \frac{6(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{4}ln(10)} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{3}ln(10)arcsin^{2}(x)} + \frac{2*-3}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} + \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{xln(10)arcsin^{2}(x)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{3}{2}}xln^{2}(10)(10)arcsin^{2}(x)} - \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}xln(10)} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{3}ln(10)arcsin^{2}(x)} + \frac{4*-3}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} + \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{4(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{4*-2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{3}(x)} + \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}(10)(10)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}}x^{2}ln(10)} + \frac{3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x}{ln(10)arcsin^{2}(x)} + \frac{3}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} + \frac{3x*-0}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{3x(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{3}(x)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}ln(10)arcsin^{3}(x)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(10)(10)arcsin^{3}(x)} - \frac{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}}ln(10)} - \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})}{ln(10)arcsin^{3}(x)} - \frac{4*-0}{(-x^{2} + 1)^{2}ln^{2}(10)(10)arcsin^{3}(x)} - \frac{4(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln(10)} + \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{x^{2}ln(10)arcsin^{3}(x)} + \frac{2*-2}{(-x^{2} + 1)x^{3}ln(10)arcsin^{3}(x)} + \frac{2*-0}{(-x^{2} + 1)x^{2}ln^{2}(10)(10)arcsin^{3}(x)} + \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)x^{2}ln(10)} + \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{4}(x)} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)xln(10)arcsin^{4}(x)} + \frac{6*-1}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{4}(x)} + \frac{6*-0}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln^{2}(10)(10)arcsin^{4}(x)} + \frac{6(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln(10)}\\=&\frac{-6}{x^{4}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4}{(-x^{2} + 1)^{\frac{3}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{18}{(-x^{2} + 1)x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{18}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{24x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{18}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{24}{(-x^{2} + 1)^{\frac{3}{2}}xln{10}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{54}{(-x^{2} + 1)^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{48}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{36}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{4}(x)} + \frac{24}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln{10}arcsin^{4}(x)} - \frac{24}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)xln{10}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{12}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln{10}arcsin^{4}(x)} - \frac{30x^{3}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{18xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{72x^{2}lg(x)}{(-x^{2} + 1)^{3}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{78x}{(-x^{2} + 1)^{3}ln{10}arcsin^{3}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{24xlg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{72xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{18lg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{48xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{108x^{2}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{4}(x)} - \frac{74xlg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} + \frac{54x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{3}arcsin^{4}(x)} + \frac{60x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}ln{10}arcsin^{2}(x)} + \frac{18}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} + \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln{10}arcsin^{2}(x)} - \frac{150x^{3}lg(x)}{(-x^{2} + 1)^{4}arcsin^{3}(x)} - \frac{18x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{3}(x)} + \frac{120lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{6}(x)sqrt(-x^{2} + 1)} - \frac{24xlg(x)}{(-x^{2} + 1)^{3}arcsin^{5}(x)} + \frac{18lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} - \frac{24xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{5}(x)} + \frac{12lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} - \frac{48xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)} + \frac{105x^{4}lg(x)}{(-x^{2} + 1)^{\frac{9}{2}}arcsin^{2}(x)} + \frac{90x^{2}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} - \frac{30x^{3}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{7}{2}}arcsin^{3}(x)} + \frac{9lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{18xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} + \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{3}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} - \frac{24}{x^{5}ln(10)arcsin(x)} - \frac{6}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} + \frac{8}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{18}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} - \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{3}(x)} - \frac{3}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}xln(10)arcsin^{3}(x)} + \frac{12}{(-x^{2} + 1)^{2}xln(10)arcsin^{3}(x)} - \frac{12}{(-x^{2} + 1)x^{3}ln(10)arcsin^{3}(x)} - \frac{12}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{4}(x)} + \frac{15x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}ln(10)arcsin^{2}(x)} - \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{3}(x)} - \frac{24x}{(-x^{2} + 1)^{3}ln(10)arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln(10)arcsin^{4}(x)} + \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln(10)arcsin^{4}(x)} - \frac{6}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)x^{2}ln(10)arcsin^{4}(x)} + \frac{18}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{4}(x)} - \frac{6}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln(10)arcsin^{4}(x)} - \frac{24}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{5}(x)}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{lg(x)}{sqrt(1 - xx)} - \frac{arcsin(x)}{(ln(10)x)}){\frac{1}{arcsin(x)}}^{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{lg(x)}{arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{1}{xln(10)arcsin(x)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{lg(x)}{arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{1}{xln(10)arcsin(x)}\right)}{dx}\\=&\frac{1}{ln{10}(x)arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{sqrt(-x^{2} + 1)} + \frac{lg(x)*-(-2x + 0)*\frac{1}{2}}{arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{-1}{x^{2}ln(10)arcsin(x)} - \frac{-0}{xln^{2}(10)(10)arcsin(x)} - \frac{(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{xln(10)}\\=&\frac{1}{xln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{1}{x^{2}ln(10)arcsin(x)} + \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{2}(x)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{1}{xln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{1}{x^{2}ln(10)arcsin(x)} + \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{2}(x)}\right)}{dx}\\=&\frac{-1}{x^{2}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{-0}{xln^{2}{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{xln{10}sqrt(-x^{2} + 1)} + \frac{-(-2x + 0)*\frac{1}{2}}{xln{10}arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}sqrt(-x^{2} + 1)} - \frac{2lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{arcsin^{2}(x)} + \frac{lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} + \frac{x}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{xlg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} + \frac{-2}{x^{3}ln(10)arcsin(x)} + \frac{-0}{x^{2}ln^{2}(10)(10)arcsin(x)} + \frac{(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{2}ln(10)} + \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{xln(10)arcsin^{2}(x)} + \frac{-1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} + \frac{-0}{(-x^{2} + 1)^{\frac{1}{2}}xln^{2}(10)(10)arcsin^{2}(x)} + \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)}\\=&\frac{-1}{x^{2}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{2xlg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{3x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2}{x^{3}ln(10)arcsin(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{2}(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-1}{x^{2}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{2xlg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{3x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{2}(x)} - \frac{2xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2}{x^{3}ln(10)arcsin(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{2}(x)} - \frac{1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)}\right)}{dx}\\=&\frac{--2}{x^{3}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{-0}{x^{2}ln^{2}{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{2}ln{10}sqrt(-x^{2} + 1)} - \frac{-(-2x + 0)*\frac{1}{2}}{x^{2}ln{10}arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}xln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}sqrt(-x^{2} + 1)} - \frac{2*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{ln{10}arcsin^{2}(x)} + \frac{2*-0}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}{10}arcsin^{2}(x)} + \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2x}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2xlg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} - \frac{2xlg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}xln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}sqrt(-x^{2} + 1)} - \frac{2*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}sqrt(-x^{2} + 1)} + \frac{6lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} - \frac{2x}{(-x^{2} + 1)^{2}ln{10}(x)arcsin^{3}(x)} - \frac{2xlg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}} + \frac{3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}lg(x)}{arcsin^{2}(x)} + \frac{3*2xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{3x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{3x^{2}lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})lg(x)}{arcsin^{2}(x)} + \frac{1}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)} - \frac{2xlg(x)(\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{2*-3}{x^{4}ln(10)arcsin(x)} - \frac{2*-0}{x^{3}ln^{2}(10)(10)arcsin(x)} - \frac{2(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{3}ln(10)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln(10)arcsin^{2}(x)} - \frac{-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}(10)(10)arcsin^{2}(x)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)} + \frac{(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{ln(10)arcsin^{2}(x)} + \frac{-0}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)} - \frac{(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln(10)arcsin^{2}(x)} - \frac{-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}(10)(10)arcsin^{2}(x)} - \frac{(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{3}(x)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln^{2}(10)(10)arcsin^{3}(x)} - \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)}\\=&\frac{2}{x^{3}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{8}{(-x^{2} + 1)^{2}ln{10}arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} - \frac{24lg(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} - \frac{4lg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{15x^{3}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} + \frac{9xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6}{x^{4}ln(10)arcsin(x)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}xln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{3x}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{3}(x)} - \frac{4}{(-x^{2} + 1)^{2}ln(10)arcsin^{3}(x)} + \frac{2}{(-x^{2} + 1)x^{2}ln(10)arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{4}(x)}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{2}{x^{3}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{8}{(-x^{2} + 1)^{2}ln{10}arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} - \frac{24lg(x)}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} - \frac{4lg(x)}{(-x^{2} + 1)^{2}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{15x^{3}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} + \frac{9xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{6x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{2lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} + \frac{6xlg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6}{x^{4}ln(10)arcsin(x)} + \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}xln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{3x}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{3}(x)} - \frac{4}{(-x^{2} + 1)^{2}ln(10)arcsin^{3}(x)} + \frac{2}{(-x^{2} + 1)x^{2}ln(10)arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{4}(x)}\right)}{dx}\\=&\frac{2*-3}{x^{4}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2*-0}{x^{3}ln^{2}{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} + \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{3}ln{10}sqrt(-x^{2} + 1)} + \frac{2*-(-2x + 0)*\frac{1}{2}}{x^{3}ln{10}arcsin^{2}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2*-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}sqrt(-x^{2} + 1)} + \frac{2*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{6(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6*-0}{(-x^{2} + 1)^{\frac{3}{2}}ln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}sqrt(-x^{2} + 1)} - \frac{6*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{2}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4*-2}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}sqrt(-x^{2} + 1)} + \frac{4*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12*-1}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln^{2}{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}sqrt(-x^{2} + 1)} + \frac{12*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{8(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})}{ln{10}arcsin^{3}(x)} - \frac{8*-0}{(-x^{2} + 1)^{2}ln^{2}{10}arcsin^{3}(x)} - \frac{8(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln{10}} + \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{xln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6*-1}{(-x^{2} + 1)x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6*-0}{(-x^{2} + 1)xln^{2}{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)xln{10}sqrt(-x^{2} + 1)} + \frac{6*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)xln{10}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{3}(x)} - \frac{4(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}ln{10}arcsin^{3}(x)} - \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}{10}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{3}{2}}ln{10}} - \frac{6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}lg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6*2xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6x^{2}}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{6x^{2}lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}sqrt(-x^{2} + 1)} - \frac{6x^{2}lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})lg(x)}{arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{2lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} - \frac{2lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}sqrt(-x^{2} + 1)} + \frac{6xlg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{12(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12lg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12x}{(-x^{2} + 1)^{2}ln{10}(x)arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{12xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}sqrt(-x^{2} + 1)} + \frac{12xlg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)^{2}arcsin^{4}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} - \frac{18(\frac{-3(-2x + 0)}{(-x^{2} + 1)^{4}})x^{2}lg(x)}{arcsin^{3}(x)} - \frac{18*2xlg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} - \frac{18x^{2}}{(-x^{2} + 1)^{3}ln{10}(x)arcsin^{3}(x)} - \frac{18x^{2}lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{3}} + \frac{9(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x}{ln{10}arcsin^{2}(x)} + \frac{9}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} + \frac{9x*-0}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}{10}arcsin^{2}(x)} + \frac{9x(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}} - \frac{24(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{24(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{24}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{24lg(x)(\frac{-5(1)}{arcsin^{6}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}sqrt(-x^{2} + 1)} - \frac{24lg(x)*-(-2x + 0)*\frac{1}{2}}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})xlg(x)}{arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} + \frac{6x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{4}(x)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})lg(x)}{arcsin^{3}(x)} - \frac{4}{(-x^{2} + 1)^{2}ln{10}(x)arcsin^{3}(x)} - \frac{4lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{6(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln{10}(x)arcsin^{4}(x)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}} + \frac{15(\frac{\frac{-7}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{9}{2}}})x^{3}lg(x)}{arcsin^{2}(x)} + \frac{15*3x^{2}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} + \frac{15x^{3}}{(-x^{2} + 1)^{\frac{7}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{15x^{3}lg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})xlg(x)}{arcsin^{2}(x)} + \frac{9lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{2}(x)} + \frac{9xlg(x)(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}} - \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})x^{2}lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{6(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{6*2xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} - \frac{6x^{2}}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln{10}(x)arcsin^{3}(x)} - \frac{6x^{2}lg(x)(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}arcsin^{3}(x)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{3}(x)} - \frac{2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}(x)arcsin^{3}(x)} - \frac{2lg(x)(\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{6(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})xlg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6x}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln{10}(x)arcsin^{4}(x)} + \frac{6xlg(x)(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}} + \frac{6*-4}{x^{5}ln(10)arcsin(x)} + \frac{6*-0}{x^{4}ln^{2}(10)(10)arcsin(x)} + \frac{6(\frac{-(1)}{arcsin^{2}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{x^{4}ln(10)} + \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{3}ln(10)arcsin^{2}(x)} + \frac{2*-3}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} + \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{xln(10)arcsin^{2}(x)} - \frac{2*-1}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{3}{2}}xln^{2}(10)(10)arcsin^{2}(x)} - \frac{2(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{3}{2}}xln(10)} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{x^{3}ln(10)arcsin^{2}(x)} + \frac{4*-3}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} + \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{4(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{4(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{3}(x)} + \frac{4*-2}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{3}(x)} + \frac{4*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln^{2}(10)(10)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}}x^{2}ln(10)} + \frac{3(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x}{ln(10)arcsin^{2}(x)} + \frac{3}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} + \frac{3x*-0}{(-x^{2} + 1)^{\frac{5}{2}}ln^{2}(10)(10)arcsin^{2}(x)} + \frac{3x(\frac{-2(1)}{arcsin^{3}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)} - \frac{2(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)^{\frac{3}{2}}ln(10)arcsin^{3}(x)} - \frac{2(\frac{\frac{-3}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{5}{2}}})}{(-x^{2} + 1)^{\frac{1}{2}}ln(10)arcsin^{3}(x)} - \frac{2*-0}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln^{2}(10)(10)arcsin^{3}(x)} - \frac{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}}ln(10)} - \frac{4(\frac{-2(-2x + 0)}{(-x^{2} + 1)^{3}})}{ln(10)arcsin^{3}(x)} - \frac{4*-0}{(-x^{2} + 1)^{2}ln^{2}(10)(10)arcsin^{3}(x)} - \frac{4(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)^{2}ln(10)} + \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{x^{2}ln(10)arcsin^{3}(x)} + \frac{2*-2}{(-x^{2} + 1)x^{3}ln(10)arcsin^{3}(x)} + \frac{2*-0}{(-x^{2} + 1)x^{2}ln^{2}(10)(10)arcsin^{3}(x)} + \frac{2(\frac{-3(1)}{arcsin^{4}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)x^{2}ln(10)} + \frac{6(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})}{(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{4}(x)} + \frac{6(\frac{\frac{-1}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{3}{2}}})}{(-x^{2} + 1)xln(10)arcsin^{4}(x)} + \frac{6*-1}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{4}(x)} + \frac{6*-0}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln^{2}(10)(10)arcsin^{4}(x)} + \frac{6(\frac{-4(1)}{arcsin^{5}(x)((1 - (x)^{2})^{\frac{1}{2}})})}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln(10)}\\=&\frac{-6}{x^{4}ln{10}arcsin^{2}(x)sqrt(-x^{2} + 1)} - \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{4}{(-x^{2} + 1)^{\frac{3}{2}}xln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{18}{(-x^{2} + 1)x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{18}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{24x}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{18}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{24}{(-x^{2} + 1)^{\frac{3}{2}}xln{10}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{54}{(-x^{2} + 1)^{2}ln{10}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{48}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}xln{10}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{36}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{4}(x)} + \frac{24}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln{10}arcsin^{4}(x)} - \frac{24}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)xln{10}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{12}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln{10}arcsin^{4}(x)} - \frac{30x^{3}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} - \frac{18xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)sqrt(-x^{2} + 1)} + \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} + \frac{72x^{2}lg(x)}{(-x^{2} + 1)^{3}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{78x}{(-x^{2} + 1)^{3}ln{10}arcsin^{3}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{24xlg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} - \frac{72xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{18lg(x)}{(-x^{2} + 1)^{2}arcsin^{4}(x)sqrt(-x^{2} + 1)} - \frac{48xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{5}(x)sqrt(-x^{2} + 1)} + \frac{108x^{2}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{4}(x)} - \frac{74xlg(x)}{(-x^{2} + 1)^{3}arcsin^{3}(x)} + \frac{54x^{2}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{3}arcsin^{4}(x)} + \frac{60x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}ln{10}arcsin^{2}(x)} + \frac{18}{(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{2}(x)} + \frac{2}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln{10}arcsin^{2}(x)} - \frac{150x^{3}lg(x)}{(-x^{2} + 1)^{4}arcsin^{3}(x)} - \frac{18x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln{10}arcsin^{3}(x)} + \frac{120lg(x)}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{6}(x)sqrt(-x^{2} + 1)} - \frac{24xlg(x)}{(-x^{2} + 1)^{3}arcsin^{5}(x)} + \frac{18lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{4}(x)} - \frac{24xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{5}(x)} + \frac{12lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}arcsin^{4}(x)} - \frac{48xlg(x)}{(-x^{2} + 1)^{\frac{5}{2}}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{5}(x)} + \frac{105x^{4}lg(x)}{(-x^{2} + 1)^{\frac{9}{2}}arcsin^{2}(x)} + \frac{90x^{2}lg(x)}{(-x^{2} + 1)^{\frac{7}{2}}arcsin^{2}(x)} - \frac{30x^{3}lg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{7}{2}}arcsin^{3}(x)} + \frac{9lg(x)}{(-x^{2} + 1)^{\frac{5}{2}}arcsin^{2}(x)} - \frac{18xlg(x)}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}arcsin^{3}(x)} + \frac{18x^{2}lg(x)}{(-x^{2} + 1)^{3}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} + \frac{6lg(x)}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}arcsin^{4}(x)} - \frac{24}{x^{5}ln(10)arcsin(x)} - \frac{6}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} + \frac{8}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln(10)arcsin^{2}(x)} - \frac{18}{(-x^{2} + 1)^{\frac{1}{2}}x^{4}ln(10)arcsin^{2}(x)} - \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{1}{2}}x^{3}ln(10)arcsin^{3}(x)} - \frac{3}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{2}(x)} + \frac{4}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{3}{2}}xln(10)arcsin^{3}(x)} + \frac{12}{(-x^{2} + 1)^{2}xln(10)arcsin^{3}(x)} - \frac{12}{(-x^{2} + 1)x^{3}ln(10)arcsin^{3}(x)} - \frac{12}{(-x^{2} + 1)(-x^{2} + 1)^{\frac{1}{2}}x^{2}ln(10)arcsin^{4}(x)} + \frac{15x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}ln(10)arcsin^{2}(x)} - \frac{6x}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{3}(x)} - \frac{24x}{(-x^{2} + 1)^{3}ln(10)arcsin^{3}(x)} + \frac{6}{(-x^{2} + 1)^{2}(-x^{2} + 1)^{\frac{1}{2}}ln(10)arcsin^{4}(x)} + \frac{12}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)^{2}ln(10)arcsin^{4}(x)} - \frac{6}{(-x^{2} + 1)^{\frac{1}{2}}(-x^{2} + 1)x^{2}ln(10)arcsin^{4}(x)} + \frac{18}{(-x^{2} + 1)^{\frac{5}{2}}ln(10)arcsin^{4}(x)} - \frac{6}{(-x^{2} + 1)^{\frac{3}{2}}x^{2}ln(10)arcsin^{4}(x)} - \frac{24}{(-x^{2} + 1)^{\frac{3}{2}}(-x^{2} + 1)^{\frac{1}{2}}xln(10)arcsin^{5}(x)}\\ \end{split}\end{equation} \]
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