本次共计算 1 个题目：每一题对 x 求 3 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数sqrt(\frac{(-4{x}^{4} - 8{x}^{3} + 578{x}^{2} + 1734x + 1293.75)}{64}) 关于 x 的 3 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( sqrt(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)\right)}{dx}\\=&\frac{(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)*0.5}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}}\\=&\frac{-0.125x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} - \frac{0.1875x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + \frac{9.03125x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + \frac{13.546875}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{-0.125x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} - \frac{0.1875x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + \frac{9.03125x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + \frac{13.546875}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}}\right)}{dx}\\=&-0.125(\frac{-0.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}})x^{3} - \frac{0.125*3x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} - 0.1875(\frac{-0.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}})x^{2} - \frac{0.1875*2x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + 9.03125(\frac{-0.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}})x + \frac{9.03125}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + 13.546875(\frac{-0.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}})\\=&\frac{-0.015625x^{6}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.0234375x^{5}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.12890625x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.375x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} - \frac{0.0234375x^{5}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.03515625x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{2.5400390625x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.375x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + \frac{1.12890625x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{81.5634765625x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{122.34521484375x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{2.5400390625x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{122.34521484375x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{183.517822265625}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{9.03125}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{-0.015625x^{6}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.0234375x^{5}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.12890625x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.375x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} - \frac{0.0234375x^{5}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.03515625x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{2.5400390625x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{0.375x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + \frac{1.12890625x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{81.5634765625x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{122.34521484375x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{1.693359375x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{2.5400390625x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{122.34521484375x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - \frac{183.517822265625}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + \frac{9.03125}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}}\right)}{dx}\\=&-0.015625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{6} - \frac{0.015625*6x^{5}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 0.0234375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{5} - \frac{0.0234375*5x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + 1.12890625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{4} + \frac{1.12890625*4x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + 1.693359375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{3} + \frac{1.693359375*3x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 0.375(\frac{-0.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}})x^{2} - \frac{0.375*2x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} - 0.0234375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{5} - \frac{0.0234375*5x^{4}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 0.03515625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{4} - \frac{0.03515625*4x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + 1.693359375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{3} + \frac{1.693359375*3x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + 2.5400390625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{2} + \frac{2.5400390625*2x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 0.375(\frac{-0.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}})x - \frac{0.375}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{1}{2}}} + 1.12890625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{4} + \frac{1.12890625*4x^{3}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + 1.693359375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{3} + \frac{1.693359375*3x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 81.5634765625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{2} - \frac{81.5634765625*2x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 122.34521484375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x - \frac{122.34521484375}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + 1.693359375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{3} + \frac{1.693359375*3x^{2}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} + 2.5400390625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x^{2} + \frac{2.5400390625*2x}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 122.34521484375(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}})x - \frac{122.34521484375}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 183.517822265625(\frac{-1.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}}) + 9.03125(\frac{-0.5(-0.0625*4x^{3} - 0.125*3x^{2} + 9.03125*2x + 27.09375 + 0)}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}})\\=&\frac{-0.005859375x^{9}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}} - \frac{0.0087890625x^{8}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}} + \frac{0.42333984375x^{7}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}} + \frac{0.635009765625x^{6}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{5}{2}}} - \frac{0.09375x^{5}}{(-0.0625x^{4} - 0.125x^{3} + 9.03125x^{2} + 27.09375x + 20.21484375)^{\frac{3}{2}}} - 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