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