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。\[ \begin{equation}\begin{split}【1/1】求函数{x}^{2}(cos(\frac{1}{({x}^{2})})) 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = x^{2}cos(\frac{1}{x^{2}})\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( x^{2}cos(\frac{1}{x^{2}})\right)}{dx}\\=&2xcos(\frac{1}{x^{2}}) + \frac{x^{2}*-sin(\frac{1}{x^{2}})*-2}{x^{3}}\\=&2xcos(\frac{1}{x^{2}}) + \frac{2sin(\frac{1}{x^{2}})}{x}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 2xcos(\frac{1}{x^{2}}) + \frac{2sin(\frac{1}{x^{2}})}{x}\right)}{dx}\\=&2cos(\frac{1}{x^{2}}) + \frac{2x*-sin(\frac{1}{x^{2}})*-2}{x^{3}} + \frac{2*-sin(\frac{1}{x^{2}})}{x^{2}} + \frac{2cos(\frac{1}{x^{2}})*-2}{xx^{3}}\\=&2cos(\frac{1}{x^{2}}) + \frac{2sin(\frac{1}{x^{2}})}{x^{2}} - \frac{4cos(\frac{1}{x^{2}})}{x^{4}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!