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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{{(sin(x))}^{2}}{(25 - 24cos(x))} 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{sin^{2}(x)}{(-24cos(x) + 25)}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( \frac{sin^{2}(x)}{(-24cos(x) + 25)}\right)}{dx}\\=&(\frac{-(-24*-sin(x) + 0)}{(-24cos(x) + 25)^{2}})sin^{2}(x) + \frac{2sin(x)cos(x)}{(-24cos(x) + 25)}\\=&\frac{2sin(x)cos(x)}{(-24cos(x) + 25)} - \frac{24sin^{3}(x)}{(-24cos(x) + 25)^{2}}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{2sin(x)cos(x)}{(-24cos(x) + 25)} - \frac{24sin^{3}(x)}{(-24cos(x) + 25)^{2}}\right)}{dx}\\=&2(\frac{-(-24*-sin(x) + 0)}{(-24cos(x) + 25)^{2}})sin(x)cos(x) + \frac{2cos(x)cos(x)}{(-24cos(x) + 25)} + \frac{2sin(x)*-sin(x)}{(-24cos(x) + 25)} - 24(\frac{-2(-24*-sin(x) + 0)}{(-24cos(x) + 25)^{3}})sin^{3}(x) - \frac{24*3sin^{2}(x)cos(x)}{(-24cos(x) + 25)^{2}}\\=&\frac{-120sin^{2}(x)cos(x)}{(-24cos(x) + 25)^{2}} + \frac{2cos^{2}(x)}{(-24cos(x) + 25)} - \frac{2sin^{2}(x)}{(-24cos(x) + 25)} + \frac{1152sin^{4}(x)}{(-24cos(x) + 25)^{3}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!