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