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