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