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。
\[ \begin{equation}\begin{split}【1/1】求函数arctan(x) - arccos(\frac{2x}{(1 + xx)}) 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = arctan(x) - arccos(\frac{2x}{(x^{2} + 1)})\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( arctan(x) - arccos(\frac{2x}{(x^{2} + 1)})\right)}{dx}\\=&(\frac{(1)}{(1 + (x)^{2})}) - (\frac{-(2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x + \frac{2}{(x^{2} + 1)})}{((1 - (\frac{2x}{(x^{2} + 1)})^{2})^{\frac{1}{2}})})\\=&\frac{-4x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)} + \frac{1}{(x^{2} + 1)}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-4x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)} + \frac{1}{(x^{2} + 1)}\right)}{dx}\\=&\frac{-4(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})x^{2}}{(x^{2} + 1)^{2}} - \frac{4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{4*2x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} + \frac{2(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})}{(x^{2} + 1)} + \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + (\frac{-(2x + 0)}{(x^{2} + 1)^{2}})\\=&\frac{32x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{5}} - \frac{32x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{4}} + \frac{16x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{8x}{(x^{2} + 1)^{2}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{8x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{3}} - \frac{4x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2x}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{32x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{5}} - \frac{32x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{4}} + \frac{16x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{8x}{(x^{2} + 1)^{2}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{8x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{3}} - \frac{4x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{2x}{(x^{2} + 1)^{2}}\right)}{dx}\\=&\frac{32(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x^{5}}{(x^{2} + 1)^{5}} + \frac{32(\frac{-5(2x + 0)}{(x^{2} + 1)^{6}})x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} + \frac{32*5x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{5}} - \frac{32(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x^{3}}{(x^{2} + 1)^{4}} - \frac{32(\frac{-4(2x + 0)}{(x^{2} + 1)^{5}})x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{32*3x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{4}} + \frac{16(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})x^{3}}{(x^{2} + 1)^{3}} + \frac{16(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{16*3x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{8(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{8(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})x}{(x^{2} + 1)^{2}} - \frac{8}{(x^{2} + 1)^{2}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{8(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x}{(x^{2} + 1)^{3}} + \frac{8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} + \frac{8}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{3}} - \frac{4(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})x}{(x^{2} + 1)^{2}} - \frac{4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{4}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x - \frac{2}{(x^{2} + 1)^{2}}\\=&\frac{-768x^{8}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{8}} + \frac{1152x^{6}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{7}} - \frac{448x^{6}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{6}} + \frac{224x^{4}}{(x^{2} + 1)^{5}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{576x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{6}} + \frac{352x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{5}} - \frac{128x^{2}}{(x^{2} + 1)^{4}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{96x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{4}} + \frac{80x^{2}}{(x^{2} + 1)^{3}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{64x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{4}} + \frac{96x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{5}} + \frac{16x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} + \frac{8}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{3}} + \frac{8x^{2}}{(x^{2} + 1)^{3}} - \frac{4}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{8}{(x^{2} + 1)^{2}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{2}{(x^{2} + 1)^{2}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{-768x^{8}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{8}} + \frac{1152x^{6}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{7}} - \frac{448x^{6}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{6}} + \frac{224x^{4}}{(x^{2} + 1)^{5}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{576x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{6}} + \frac{352x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{5}} - \frac{128x^{2}}{(x^{2} + 1)^{4}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{96x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{4}} + \frac{80x^{2}}{(x^{2} + 1)^{3}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{64x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{4}} + \frac{96x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{5}} + \frac{16x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} + \frac{8}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{3}} + \frac{8x^{2}}{(x^{2} + 1)^{3}} - \frac{4}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{2}} - \frac{8}{(x^{2} + 1)^{2}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{2}{(x^{2} + 1)^{2}}\right)}{dx}\\=&\frac{-768(\frac{\frac{-5}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}})x^{8}}{(x^{2} + 1)^{8}} - \frac{768(\frac{-8(2x + 0)}{(x^{2} + 1)^{9}})x^{8}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} - \frac{768*8x^{7}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{8}} + \frac{1152(\frac{\frac{-5}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}})x^{6}}{(x^{2} + 1)^{7}} + \frac{1152(\frac{-7(2x + 0)}{(x^{2} + 1)^{8}})x^{6}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} + \frac{1152*6x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{7}} - \frac{448(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x^{6}}{(x^{2} + 1)^{6}} - \frac{448(\frac{-6(2x + 0)}{(x^{2} + 1)^{7}})x^{6}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{448*6x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{6}} + \frac{224(\frac{-5(2x + 0)}{(x^{2} + 1)^{6}})x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} + \frac{224(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x^{4}}{(x^{2} + 1)^{5}} + \frac{224*4x^{3}}{(x^{2} + 1)^{5}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{576(\frac{\frac{-5}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}})x^{4}}{(x^{2} + 1)^{6}} - \frac{576(\frac{-6(2x + 0)}{(x^{2} + 1)^{7}})x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} - \frac{576*4x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{6}} + \frac{352(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x^{4}}{(x^{2} + 1)^{5}} + \frac{352(\frac{-5(2x + 0)}{(x^{2} + 1)^{6}})x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} + \frac{352*4x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{5}} - \frac{128(\frac{-4(2x + 0)}{(x^{2} + 1)^{5}})x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{128(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x^{2}}{(x^{2} + 1)^{4}} - \frac{128*2x}{(x^{2} + 1)^{4}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{96(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})x^{4}}{(x^{2} + 1)^{4}} - \frac{96(\frac{-4(2x + 0)}{(x^{2} + 1)^{5}})x^{4}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{96*4x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{4}} + \frac{80(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{80(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})x^{2}}{(x^{2} + 1)^{3}} + \frac{80*2x}{(x^{2} + 1)^{3}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{64(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})x^{2}}{(x^{2} + 1)^{4}} - \frac{64(\frac{-4(2x + 0)}{(x^{2} + 1)^{5}})x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{64*2x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{4}} + \frac{96(\frac{\frac{-5}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}})x^{2}}{(x^{2} + 1)^{5}} + \frac{96(\frac{-5(2x + 0)}{(x^{2} + 1)^{6}})x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} + \frac{96*2x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{5}} + \frac{16(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})x^{2}}{(x^{2} + 1)^{3}} + \frac{16(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{16*2x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} + \frac{8(\frac{\frac{-3}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}})}{(x^{2} + 1)^{3}} + \frac{8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} + 8(\frac{-3(2x + 0)}{(x^{2} + 1)^{4}})x^{2} + \frac{8*2x}{(x^{2} + 1)^{3}} - \frac{4(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})}{(x^{2} + 1)^{2}} - \frac{4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{8(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} - \frac{8(\frac{\frac{-1}{2}(-4(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})x^{2} - \frac{4*2x}{(x^{2} + 1)^{2}} + 0)}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}})}{(x^{2} + 1)^{2}} - 2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})\\=&\frac{30720x^{11}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}(x^{2} + 1)^{11}} - \frac{61440x^{9}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}(x^{2} + 1)^{10}} + \frac{23040x^{9}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{9}} - \frac{11520x^{7}}{(x^{2} + 1)^{8}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} + \frac{46080x^{7}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}(x^{2} + 1)^{9}} - \frac{29952x^{7}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{8}} + \frac{12672x^{5}}{(x^{2} + 1)^{7}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} + \frac{6144x^{7}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{7}} - \frac{5568x^{5}}{(x^{2} + 1)^{6}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} + \frac{1504x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{5}} - \frac{15360x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}(x^{2} + 1)^{8}} + \frac{12672x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{7}} - \frac{3840x^{3}}{(x^{2} + 1)^{6}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} - \frac{4032x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{6}} + \frac{2816x^{3}}{(x^{2} + 1)^{5}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} - \frac{320x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}(x^{2} + 1)^{4}} + \frac{768x^{5}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{5}} - \frac{864x^{3}}{(x^{2} + 1)^{4}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{176x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{3}} - \frac{1920x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{6}} - \frac{160x}{(x^{2} + 1)^{4}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{3}{2}}} + \frac{1920x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{7}{2}}(x^{2} + 1)^{7}} + \frac{192x}{(x^{2} + 1)^{5}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}} - \frac{96x^{3}}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}(x^{2} + 1)^{4}} + \frac{64x}{(x^{2} + 1)^{3}(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{1}{2}}} + \frac{96x}{(\frac{-4x^{2}}{(x^{2} + 1)^{2}} + 1)^{\frac{5}{2}}(x^{2} + 1)^{5}} - \frac{48x^{3}}{(x^{2} + 1)^{4}} + \frac{24x}{(x^{2} + 1)^{3}}\\ \end{split}\end{equation} \]

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