本次共计算 1 个题目：每一题对 x 求 1 阶导数。
    注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{(\frac{({x}^{2} - 4)}{({x}^{2} + 4)})}^{4} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{x^{8}}{(x^{2} + 4)^{4}} - \frac{16x^{6}}{(x^{2} + 4)^{4}} + \frac{96x^{4}}{(x^{2} + 4)^{4}} - \frac{256x^{2}}{(x^{2} + 4)^{4}} + \frac{256}{(x^{2} + 4)^{4}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{x^{8}}{(x^{2} + 4)^{4}} - \frac{16x^{6}}{(x^{2} + 4)^{4}} + \frac{96x^{4}}{(x^{2} + 4)^{4}} - \frac{256x^{2}}{(x^{2} + 4)^{4}} + \frac{256}{(x^{2} + 4)^{4}}\right)}{dx}\\=&(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{8} + \frac{8x^{7}}{(x^{2} + 4)^{4}} - 16(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{6} - \frac{16*6x^{5}}{(x^{2} + 4)^{4}} + 96(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{4} + \frac{96*4x^{3}}{(x^{2} + 4)^{4}} - 256(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})x^{2} - \frac{256*2x}{(x^{2} + 4)^{4}} + 256(\frac{-4(2x + 0)}{(x^{2} + 4)^{5}})\\=&\frac{-8x^{9}}{(x^{2} + 4)^{5}} + \frac{8x^{7}}{(x^{2} + 4)^{4}} + \frac{128x^{7}}{(x^{2} + 4)^{5}} - \frac{96x^{5}}{(x^{2} + 4)^{4}} - \frac{768x^{5}}{(x^{2} + 4)^{5}} + \frac{384x^{3}}{(x^{2} + 4)^{4}} + \frac{2048x^{3}}{(x^{2} + 4)^{5}} - \frac{512x}{(x^{2} + 4)^{4}} - \frac{2048x}{(x^{2} + 4)^{5}}\\ \end{split}\end{equation} \]

你的问题在这里没有得到解决？请到 热门难题 里面看看吧！