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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(sqrt(8 - x)xsqrt(x + 8) + 64arcsin(\frac{x}{8}))}{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{2}xsqrt(x + 8)sqrt(-x + 8) + 32arcsin(\frac{1}{8}x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{2}xsqrt(x + 8)sqrt(-x + 8) + 32arcsin(\frac{1}{8}x)\right)}{dx}\\=&\frac{1}{2}sqrt(x + 8)sqrt(-x + 8) + \frac{\frac{1}{2}x(1 + 0)*\frac{1}{2}sqrt(-x + 8)}{(x + 8)^{\frac{1}{2}}} + \frac{\frac{1}{2}xsqrt(x + 8)(-1 + 0)*\frac{1}{2}}{(-x + 8)^{\frac{1}{2}}} + 32(\frac{(\frac{1}{8})}{((1 - (\frac{1}{8}x)^{2})^{\frac{1}{2}})})\\=&\frac{sqrt(x + 8)sqrt(-x + 8)}{2} + \frac{xsqrt(-x + 8)}{4(x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{4(-x + 8)^{\frac{1}{2}}} + \frac{4}{(\frac{-1}{64}x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sqrt(x + 8)sqrt(-x + 8)}{2} + \frac{xsqrt(-x + 8)}{4(x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{4(-x + 8)^{\frac{1}{2}}} + \frac{4}{(\frac{-1}{64}x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{(1 + 0)*\frac{1}{2}sqrt(-x + 8)}{2(x + 8)^{\frac{1}{2}}} + \frac{sqrt(x + 8)(-1 + 0)*\frac{1}{2}}{2(-x + 8)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})xsqrt(-x + 8)}{4} + \frac{sqrt(-x + 8)}{4(x + 8)^{\frac{1}{2}}} + \frac{x(-1 + 0)*\frac{1}{2}}{4(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})xsqrt(x + 8)}{4} - \frac{sqrt(x + 8)}{4(-x + 8)^{\frac{1}{2}}} - \frac{x(1 + 0)*\frac{1}{2}}{4(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + 4(\frac{\frac{-1}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}})\\=&\frac{sqrt(-x + 8)}{2(x + 8)^{\frac{1}{2}}} - \frac{sqrt(x + 8)}{2(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} - \frac{x}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} - \frac{x}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{x}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sqrt(-x + 8)}{2(x + 8)^{\frac{1}{2}}} - \frac{sqrt(x + 8)}{2(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} - \frac{x}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} - \frac{x}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{x}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})sqrt(-x + 8)}{2} + \frac{(-1 + 0)*\frac{1}{2}}{2(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})sqrt(x + 8)}{2} - \frac{(1 + 0)*\frac{1}{2}}{2(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(1 + 0)}{(x + 8)^{\frac{5}{2}}})xsqrt(-x + 8)}{8} - \frac{sqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} - \frac{x(-1 + 0)*\frac{1}{2}}{8(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})x}{8(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})x}{8(x + 8)^{\frac{1}{2}}} - \frac{1}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 8)^{\frac{5}{2}}})xsqrt(x + 8)}{8} - \frac{sqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} - \frac{x(1 + 0)*\frac{1}{2}}{8(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})x}{8(x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})x}{8(-x + 8)^{\frac{1}{2}}} - \frac{1}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{(\frac{\frac{-3}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}})x}{16} + \frac{1}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\\=&\frac{-3sqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} + \frac{3x}{16(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3sqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} + \frac{3xsqrt(-x + 8)}{16(x + 8)^{\frac{5}{2}}} - \frac{3x}{16(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3xsqrt(x + 8)}{16(-x + 8)^{\frac{5}{2}}} - \frac{3}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{3x^{2}}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}} + \frac{1}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3sqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} + \frac{3x}{16(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3sqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} + \frac{3xsqrt(-x + 8)}{16(x + 8)^{\frac{5}{2}}} - \frac{3x}{16(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3xsqrt(x + 8)}{16(-x + 8)^{\frac{5}{2}}} - \frac{3}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{3x^{2}}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}} + \frac{1}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-3(\frac{\frac{-3}{2}(1 + 0)}{(x + 8)^{\frac{5}{2}}})sqrt(-x + 8)}{8} - \frac{3(-1 + 0)*\frac{1}{2}}{8(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-3}{2}(1 + 0)}{(x + 8)^{\frac{5}{2}}})x}{16(-x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})x}{16(x + 8)^{\frac{3}{2}}} + \frac{3}{16(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 8)^{\frac{5}{2}}})sqrt(x + 8)}{8} - \frac{3(1 + 0)*\frac{1}{2}}{8(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-5}{2}(1 + 0)}{(x + 8)^{\frac{7}{2}}})xsqrt(-x + 8)}{16} + \frac{3sqrt(-x + 8)}{16(x + 8)^{\frac{5}{2}}} + \frac{3x(-1 + 0)*\frac{1}{2}}{16(x + 8)^{\frac{5}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 8)^{\frac{5}{2}}})x}{16(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})x}{16(-x + 8)^{\frac{3}{2}}} - \frac{3}{16(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})}{8(-x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})}{8(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-5}{2}(-1 + 0)}{(-x + 8)^{\frac{7}{2}}})xsqrt(x + 8)}{16} - \frac{3sqrt(x + 8)}{16(-x + 8)^{\frac{5}{2}}} - \frac{3x(1 + 0)*\frac{1}{2}}{16(-x + 8)^{\frac{5}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})}{8(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})}{8(-x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-5}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{7}{2}}})x^{2}}{1024} + \frac{3*2x}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}} + \frac{(\frac{\frac{-3}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}})}{16}\\=&\frac{3sqrt(-x + 8)}{4(x + 8)^{\frac{5}{2}}} - \frac{3x}{8(x + 8)^{\frac{5}{2}}(-x + 8)^{\frac{1}{2}}} + \frac{3x}{32(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{3}{2}}} - \frac{3x}{8(-x + 8)^{\frac{5}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3sqrt(x + 8)}{4(-x + 8)^{\frac{5}{2}}} + \frac{3x}{32(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{3}{2}}} - \frac{15xsqrt(-x + 8)}{32(x + 8)^{\frac{7}{2}}} + \frac{3}{4(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3}{4(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{15xsqrt(x + 8)}{32(-x + 8)^{\frac{7}{2}}} + \frac{15x^{3}}{65536(\frac{-1}{64}x^{2} + 1)^{\frac{7}{2}}} + \frac{9x}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(sqrt(8 - x)xsqrt(x + 8) + 64arcsin(\frac{x}{8}))}{2} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{1}{2}xsqrt(x + 8)sqrt(-x + 8) + 32arcsin(\frac{1}{8}x)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{1}{2}xsqrt(x + 8)sqrt(-x + 8) + 32arcsin(\frac{1}{8}x)\right)}{dx}\\=&\frac{1}{2}sqrt(x + 8)sqrt(-x + 8) + \frac{\frac{1}{2}x(1 + 0)*\frac{1}{2}sqrt(-x + 8)}{(x + 8)^{\frac{1}{2}}} + \frac{\frac{1}{2}xsqrt(x + 8)(-1 + 0)*\frac{1}{2}}{(-x + 8)^{\frac{1}{2}}} + 32(\frac{(\frac{1}{8})}{((1 - (\frac{1}{8}x)^{2})^{\frac{1}{2}})})\\=&\frac{sqrt(x + 8)sqrt(-x + 8)}{2} + \frac{xsqrt(-x + 8)}{4(x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{4(-x + 8)^{\frac{1}{2}}} + \frac{4}{(\frac{-1}{64}x^{2} + 1)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{sqrt(x + 8)sqrt(-x + 8)}{2} + \frac{xsqrt(-x + 8)}{4(x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{4(-x + 8)^{\frac{1}{2}}} + \frac{4}{(\frac{-1}{64}x^{2} + 1)^{\frac{1}{2}}}\right)}{dx}\\=&\frac{(1 + 0)*\frac{1}{2}sqrt(-x + 8)}{2(x + 8)^{\frac{1}{2}}} + \frac{sqrt(x + 8)(-1 + 0)*\frac{1}{2}}{2(-x + 8)^{\frac{1}{2}}} + \frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})xsqrt(-x + 8)}{4} + \frac{sqrt(-x + 8)}{4(x + 8)^{\frac{1}{2}}} + \frac{x(-1 + 0)*\frac{1}{2}}{4(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})xsqrt(x + 8)}{4} - \frac{sqrt(x + 8)}{4(-x + 8)^{\frac{1}{2}}} - \frac{x(1 + 0)*\frac{1}{2}}{4(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + 4(\frac{\frac{-1}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}})\\=&\frac{sqrt(-x + 8)}{2(x + 8)^{\frac{1}{2}}} - \frac{sqrt(x + 8)}{2(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} - \frac{x}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} - \frac{x}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{x}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{sqrt(-x + 8)}{2(x + 8)^{\frac{1}{2}}} - \frac{sqrt(x + 8)}{2(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} - \frac{x}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{xsqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} - \frac{x}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{x}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})sqrt(-x + 8)}{2} + \frac{(-1 + 0)*\frac{1}{2}}{2(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})sqrt(x + 8)}{2} - \frac{(1 + 0)*\frac{1}{2}}{2(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(1 + 0)}{(x + 8)^{\frac{5}{2}}})xsqrt(-x + 8)}{8} - \frac{sqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} - \frac{x(-1 + 0)*\frac{1}{2}}{8(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})x}{8(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})x}{8(x + 8)^{\frac{1}{2}}} - \frac{1}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 8)^{\frac{5}{2}}})xsqrt(x + 8)}{8} - \frac{sqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} - \frac{x(1 + 0)*\frac{1}{2}}{8(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})x}{8(x + 8)^{\frac{1}{2}}} - \frac{(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})x}{8(-x + 8)^{\frac{1}{2}}} - \frac{1}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{(\frac{\frac{-3}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}})x}{16} + \frac{1}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\\=&\frac{-3sqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} + \frac{3x}{16(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3sqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} + \frac{3xsqrt(-x + 8)}{16(x + 8)^{\frac{5}{2}}} - \frac{3x}{16(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3xsqrt(x + 8)}{16(-x + 8)^{\frac{5}{2}}} - \frac{3}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{3x^{2}}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}} + \frac{1}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-3sqrt(-x + 8)}{8(x + 8)^{\frac{3}{2}}} + \frac{3x}{16(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3sqrt(x + 8)}{8(-x + 8)^{\frac{3}{2}}} + \frac{3xsqrt(-x + 8)}{16(x + 8)^{\frac{5}{2}}} - \frac{3x}{16(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3}{8(x + 8)^{\frac{1}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3xsqrt(x + 8)}{16(-x + 8)^{\frac{5}{2}}} - \frac{3}{8(-x + 8)^{\frac{1}{2}}(x + 8)^{\frac{1}{2}}} + \frac{3x^{2}}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}} + \frac{1}{16(\frac{-1}{64}x^{2} + 1)^{\frac{3}{2}}}\right)}{dx}\\=&\frac{-3(\frac{\frac{-3}{2}(1 + 0)}{(x + 8)^{\frac{5}{2}}})sqrt(-x + 8)}{8} - \frac{3(-1 + 0)*\frac{1}{2}}{8(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-3}{2}(1 + 0)}{(x + 8)^{\frac{5}{2}}})x}{16(-x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})x}{16(x + 8)^{\frac{3}{2}}} + \frac{3}{16(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 8)^{\frac{5}{2}}})sqrt(x + 8)}{8} - \frac{3(1 + 0)*\frac{1}{2}}{8(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-5}{2}(1 + 0)}{(x + 8)^{\frac{7}{2}}})xsqrt(-x + 8)}{16} + \frac{3sqrt(-x + 8)}{16(x + 8)^{\frac{5}{2}}} + \frac{3x(-1 + 0)*\frac{1}{2}}{16(x + 8)^{\frac{5}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-3}{2}(-1 + 0)}{(-x + 8)^{\frac{5}{2}}})x}{16(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})x}{16(-x + 8)^{\frac{3}{2}}} - \frac{3}{16(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})}{8(-x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})}{8(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-5}{2}(-1 + 0)}{(-x + 8)^{\frac{7}{2}}})xsqrt(x + 8)}{16} - \frac{3sqrt(x + 8)}{16(-x + 8)^{\frac{5}{2}}} - \frac{3x(1 + 0)*\frac{1}{2}}{16(-x + 8)^{\frac{5}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(-1 + 0)}{(-x + 8)^{\frac{3}{2}}})}{8(x + 8)^{\frac{1}{2}}} - \frac{3(\frac{\frac{-1}{2}(1 + 0)}{(x + 8)^{\frac{3}{2}}})}{8(-x + 8)^{\frac{1}{2}}} + \frac{3(\frac{\frac{-5}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{7}{2}}})x^{2}}{1024} + \frac{3*2x}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}} + \frac{(\frac{\frac{-3}{2}(\frac{-1}{64}*2x + 0)}{(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}})}{16}\\=&\frac{3sqrt(-x + 8)}{4(x + 8)^{\frac{5}{2}}} - \frac{3x}{8(x + 8)^{\frac{5}{2}}(-x + 8)^{\frac{1}{2}}} + \frac{3x}{32(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{3}{2}}} - \frac{3x}{8(-x + 8)^{\frac{5}{2}}(x + 8)^{\frac{1}{2}}} - \frac{3sqrt(x + 8)}{4(-x + 8)^{\frac{5}{2}}} + \frac{3x}{32(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{3}{2}}} - \frac{15xsqrt(-x + 8)}{32(x + 8)^{\frac{7}{2}}} + \frac{3}{4(x + 8)^{\frac{3}{2}}(-x + 8)^{\frac{1}{2}}} - \frac{3}{4(-x + 8)^{\frac{3}{2}}(x + 8)^{\frac{1}{2}}} - \frac{15xsqrt(x + 8)}{32(-x + 8)^{\frac{7}{2}}} + \frac{15x^{3}}{65536(\frac{-1}{64}x^{2} + 1)^{\frac{7}{2}}} + \frac{9x}{1024(\frac{-1}{64}x^{2} + 1)^{\frac{5}{2}}}\\ \end{split}\end{equation} \]
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