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