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。
\[ \begin{equation}\begin{split}【1/1】求函数(\frac{15({x}^{3})}{({(1 - {x}^{2})}^{(\frac{7}{2})})}) + \frac{9x}{({(1 - {x}^{2})}^{(\frac{5}{2})})} 关于 x 的 4 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{15x^{3}}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{15x^{3}}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9x}{(-x^{2} + 1)^{\frac{5}{2}}}\right)}{dx}\\=&15(\frac{\frac{-7}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{9}{2}}})x^{3} + \frac{15*3x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}} + 9(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})x + \frac{9}{(-x^{2} + 1)^{\frac{5}{2}}}\\=&\frac{105x^{4}}{(-x^{2} + 1)^{\frac{9}{2}}} + \frac{90x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9}{(-x^{2} + 1)^{\frac{5}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数：} \\&\frac{d\left( \frac{105x^{4}}{(-x^{2} + 1)^{\frac{9}{2}}} + \frac{90x^{2}}{(-x^{2} + 1)^{\frac{7}{2}}} + \frac{9}{(-x^{2} + 1)^{\frac{5}{2}}}\right)}{dx}\\=&105(\frac{\frac{-9}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{11}{2}}})x^{4} + \frac{105*4x^{3}}{(-x^{2} + 1)^{\frac{9}{2}}} + 90(\frac{\frac{-7}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{9}{2}}})x^{2} + \frac{90*2x}{(-x^{2} + 1)^{\frac{7}{2}}} + 9(\frac{\frac{-5}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{7}{2}}})\\=&\frac{945x^{5}}{(-x^{2} + 1)^{\frac{11}{2}}} + \frac{1050x^{3}}{(-x^{2} + 1)^{\frac{9}{2}}} + \frac{225x}{(-x^{2} + 1)^{\frac{7}{2}}}\\\\ &\color{blue}{函数的第 3 阶导数：} \\&\frac{d\left( \frac{945x^{5}}{(-x^{2} + 1)^{\frac{11}{2}}} + \frac{1050x^{3}}{(-x^{2} + 1)^{\frac{9}{2}}} + \frac{225x}{(-x^{2} + 1)^{\frac{7}{2}}}\right)}{dx}\\=&945(\frac{\frac{-11}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{13}{2}}})x^{5} + \frac{945*5x^{4}}{(-x^{2} + 1)^{\frac{11}{2}}} + 1050(\frac{\frac{-9}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{11}{2}}})x^{3} + \frac{1050*3x^{2}}{(-x^{2} + 1)^{\frac{9}{2}}} + 225(\frac{\frac{-7}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{9}{2}}})x + \frac{225}{(-x^{2} + 1)^{\frac{7}{2}}}\\=&\frac{10395x^{6}}{(-x^{2} + 1)^{\frac{13}{2}}} + \frac{14175x^{4}}{(-x^{2} + 1)^{\frac{11}{2}}} + \frac{4725x^{2}}{(-x^{2} + 1)^{\frac{9}{2}}} + \frac{225}{(-x^{2} + 1)^{\frac{7}{2}}}\\\\ &\color{blue}{函数的第 4 阶导数：} \\&\frac{d\left( \frac{10395x^{6}}{(-x^{2} + 1)^{\frac{13}{2}}} + \frac{14175x^{4}}{(-x^{2} + 1)^{\frac{11}{2}}} + \frac{4725x^{2}}{(-x^{2} + 1)^{\frac{9}{2}}} + \frac{225}{(-x^{2} + 1)^{\frac{7}{2}}}\right)}{dx}\\=&10395(\frac{\frac{-13}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{15}{2}}})x^{6} + \frac{10395*6x^{5}}{(-x^{2} + 1)^{\frac{13}{2}}} + 14175(\frac{\frac{-11}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{13}{2}}})x^{4} + \frac{14175*4x^{3}}{(-x^{2} + 1)^{\frac{11}{2}}} + 4725(\frac{\frac{-9}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{11}{2}}})x^{2} + \frac{4725*2x}{(-x^{2} + 1)^{\frac{9}{2}}} + 225(\frac{\frac{-7}{2}(-2x + 0)}{(-x^{2} + 1)^{\frac{9}{2}}})\\=&\frac{135135x^{7}}{(-x^{2} + 1)^{\frac{15}{2}}} + \frac{218295x^{5}}{(-x^{2} + 1)^{\frac{13}{2}}} + \frac{99225x^{3}}{(-x^{2} + 1)^{\frac{11}{2}}} + \frac{11025x}{(-x^{2} + 1)^{\frac{9}{2}}}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！