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。\[ \begin{equation}\begin{split}【1/1】求函数sqrt(172225 - {(x - 1500)}^{2}) 关于 x 的 2 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = sqrt(-x^{2} + 3000x - 2077775)\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( sqrt(-x^{2} + 3000x - 2077775)\right)}{dx}\\=&\frac{(-2x + 3000 + 0)*\frac{1}{2}}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}}\\=&\frac{-x}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} + \frac{1500}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}}\\\\ &\color{blue}{函数的第 2 阶导数:} \\&\frac{d\left( \frac{-x}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} + \frac{1500}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}}\right)}{dx}\\=&-(\frac{\frac{-1}{2}(-2x + 3000 + 0)}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}})x - \frac{1}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} + 1500(\frac{\frac{-1}{2}(-2x + 3000 + 0)}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}})\\=&\frac{-x^{2}}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}} + \frac{3000x}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}} - \frac{1}{(-x^{2} + 3000x - 2077775)^{\frac{1}{2}}} - \frac{2250000}{(-x^{2} + 3000x - 2077775)^{\frac{3}{2}}}\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!