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