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