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。\[ \begin{equation}\begin{split}【1/1】求函数\frac{({(\frac{(sqrt(5) + 1)}{2})}^{x} - cos(Pix){\frac{1}{(\frac{(sqrt(5) + 1)}{2})}}^{x})}{({(\frac{(sqrt(5) + 1)}{2})}^{x} - cos(Pix){\frac{1}{(\frac{(sqrt(5) + 1)}{2})}}^{(x + 2)})} 关于 x 的 1 阶导数:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = - \frac{{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})} + \frac{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})}\\&\color{blue}{函数的第 1 阶导数:}\\&\frac{d\left( - \frac{{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})} + \frac{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})}\right)}{dx}\\=& - (\frac{-(-({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}((1 + 0)ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}) + \frac{(x + 2)((\frac{-(\frac{1}{2}*0*\frac{1}{2}*5^{\frac{1}{2}} + 0)}{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{2}}))}{(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})}))cos(Pix) - {\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}*-sin(Pix)Pi + ((\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}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}}){\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix) - \frac{({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}((1)ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}) + \frac{(x)((\frac{-(\frac{1}{2}*0*\frac{1}{2}*5^{\frac{1}{2}} + 0)}{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{2}}))}{(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})}))cos(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})} - \frac{{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}*-sin(Pix)Pi}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})} + (\frac{-(-({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}((1 + 0)ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}) + \frac{(x + 2)((\frac{-(\frac{1}{2}*0*\frac{1}{2}*5^{\frac{1}{2}} + 0)}{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{2}}))}{(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})}))cos(Pix) - {\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}*-sin(Pix)Pi + ((\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}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}})(\frac{1}{2}sqrt(5) + \frac{1}{2})^{x} + \frac{((\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}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})}\\=&\frac{-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(2x + 4)}ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})cos^{2}(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}} + \frac{Pi{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(2x + 4)}sin(Pix)cos(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}} + \frac{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}ln(\frac{1}{2}sqrt(5) + \frac{1}{2})cos(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}} - \frac{{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})cos(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})} + \frac{Pi{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}sin(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})} + \frac{{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}(\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})cos(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}} - \frac{Pi{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}(\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}sin(Pix)}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}} - \frac{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{(2(x))}ln(\frac{1}{2}sqrt(5) + \frac{1}{2})}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})^{2}} + \frac{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{x}ln(\frac{1}{2}sqrt(5) + \frac{1}{2})}{(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 2)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{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!