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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{(3{x}^{4} - 6a{x}^{2} + 3{a}^{2})}{({(3{x}^{2} + a)}^{2})} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{3x^{4}}{(3x^{2} + a)^{2}} - \frac{6ax^{2}}{(3x^{2} + a)^{2}} + \frac{3a^{2}}{(3x^{2} + a)^{2}}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{3x^{4}}{(3x^{2} + a)^{2}} - \frac{6ax^{2}}{(3x^{2} + a)^{2}} + \frac{3a^{2}}{(3x^{2} + a)^{2}}\right)}{dx}\\=&3(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})x^{4} + \frac{3*4x^{3}}{(3x^{2} + a)^{2}} - 6(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})ax^{2} - \frac{6a*2x}{(3x^{2} + a)^{2}} + 3(\frac{-2(3*2x + 0)}{(3x^{2} + a)^{3}})a^{2} + 0\\=&\frac{-36x^{5}}{(3x^{2} + a)^{3}} + \frac{12x^{3}}{(3x^{2} + a)^{2}} + \frac{72ax^{3}}{(3x^{2} + a)^{3}} - \frac{12ax}{(3x^{2} + a)^{2}} - \frac{36a^{2}x}{(3x^{2} + a)^{3}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!