本次共计算 1 个题目:每一题对 x 求 2 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数\frac{ln(1 - {x}^{2})}{(1 + {x}^{2})} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{ln(-x^{2} + 1)}{(x^{2} + 1)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{ln(-x^{2} + 1)}{(x^{2} + 1)}\right)}{dx}\\=&(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})ln(-x^{2} + 1) + \frac{(-2x + 0)}{(x^{2} + 1)(-x^{2} + 1)}\\=&\frac{-2xln(-x^{2} + 1)}{(x^{2} + 1)^{2}} - \frac{2x}{(x^{2} + 1)(-x^{2} + 1)}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{-2xln(-x^{2} + 1)}{(x^{2} + 1)^{2}} - \frac{2x}{(x^{2} + 1)(-x^{2} + 1)}\right)}{dx}\\=&-2(\frac{-2(2x + 0)}{(x^{2} + 1)^{3}})xln(-x^{2} + 1) - \frac{2ln(-x^{2} + 1)}{(x^{2} + 1)^{2}} - \frac{2x(-2x + 0)}{(x^{2} + 1)^{2}(-x^{2} + 1)} - \frac{2(\frac{-(2x + 0)}{(x^{2} + 1)^{2}})x}{(-x^{2} + 1)} - \frac{2(\frac{-(-2x + 0)}{(-x^{2} + 1)^{2}})x}{(x^{2} + 1)} - \frac{2}{(x^{2} + 1)(-x^{2} + 1)}\\=&\frac{8x^{2}ln(-x^{2} + 1)}{(x^{2} + 1)^{3}} - \frac{2ln(-x^{2} + 1)}{(x^{2} + 1)^{2}} + \frac{8x^{2}}{(x^{2} + 1)^{2}(-x^{2} + 1)} - \frac{4x^{2}}{(x^{2} + 1)(-x^{2} + 1)^{2}} - \frac{2}{(x^{2} + 1)(-x^{2} + 1)}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!