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