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