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