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