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