本次共计算 1 个题目:每一题对 x 求 4 阶导数。
注意,变量是区分大小写的。\[ \begin{equation}\begin{split}【1/1】求函数ln(x)*2x - tan(x) 关于 x 的 4 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = 2xln(x) - tan(x)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( 2xln(x) - tan(x)\right)}{dx}\\=&2ln(x) + \frac{2x}{(x)} - sec^{2}(x)(1)\\=&2ln(x) - sec^{2}(x) + 2\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( 2ln(x) - sec^{2}(x) + 2\right)}{dx}\\=&\frac{2}{(x)} - 2sec^{2}(x)tan(x) + 0\\=&\frac{2}{x} - 2tan(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 3 阶导数:} \\&\frac{d\left( \frac{2}{x} - 2tan(x)sec^{2}(x)\right)}{dx}\\=&\frac{2*-1}{x^{2}} - 2sec^{2}(x)(1)sec^{2}(x) - 2tan(x)*2sec^{2}(x)tan(x)\\=&\frac{-2}{x^{2}} - 2sec^{4}(x) - 4tan^{2}(x)sec^{2}(x)\\\\ &\color{blue}{函数的第 4 阶导数:} \\&\frac{d\left( \frac{-2}{x^{2}} - 2sec^{4}(x) - 4tan^{2}(x)sec^{2}(x)\right)}{dx}\\=&\frac{-2*-2}{x^{3}} - 2*4sec^{4}(x)tan(x) - 4*2tan(x)sec^{2}(x)(1)sec^{2}(x) - 4tan^{2}(x)*2sec^{2}(x)tan(x)\\=&\frac{4}{x^{3}} - 16tan(x)sec^{4}(x) - 8tan^{3}(x)sec^{2}(x)\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!