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