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。\[ \begin{equation}\begin{split}【1/1】求函数{(\frac{(sqrt(5))}{2} - \frac{1}{2})}^{x} + {(\frac{(sqrt(5))}{2} + \frac{1}{2})}^{x} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = (\frac{1}{2}sqrt(5) - \frac{1}{2})^{x} + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( (\frac{1}{2}sqrt(5) - \frac{1}{2})^{x} + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}\right)}{dx}\\=&((\frac{1}{2}sqrt(5) - \frac{1}{2})^{x}((1)ln(\frac{1}{2}sqrt(5) - \frac{1}{2}) + \frac{(x)(\frac{1}{2}*0*\frac{1}{2}*5^{\frac{1}{2}} + 0)}{(\frac{1}{2}sqrt(5) - \frac{1}{2})})) + ((\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}((1)ln(\frac{1}{2}sqrt(5) + \frac{1}{2}) + \frac{(x)(\frac{1}{2}*0*\frac{1}{2}*5^{\frac{1}{2}} + 0)}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}))\\=&(\frac{1}{2}sqrt(5) - \frac{1}{2})^{x}ln(\frac{1}{2}sqrt(5) - \frac{1}{2}) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}ln(\frac{1}{2}sqrt(5) + \frac{1}{2})\\ \end{split}\end{equation} \]你的问题在这里没有得到解决?请到 热门难题 里面看看吧!