求导函数：
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
输入一个原函数（即需要求导的函数），然后设置需要求导的变量和求导的阶数，点击“下一步”按钮，即可获得该函数相应阶数的导函数。
注意，输入的函数支持数学函数和其它常量。
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。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{ln(({(\frac{(sqrt(5) + 1)}{2})}^{x} - cos(Pix){\frac{1}{(\frac{(sqrt(5) + 1)}{2})}}^{x}))}{ln(({(\frac{(sqrt(5) + 1)}{2})}^{(x + 1)} + cos(Pix){\frac{1}{(\frac{(sqrt(5) + 1)}{2})}}^{(x + 1)}))} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{ln(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})}{ln({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{ln(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})}{ln({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})}\right)}{dx}\\=&\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}*-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}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})ln({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})} + \frac{ln(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})*-(({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}((1 + 0)ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}) + \frac{(x + 1)((\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 + 1)}*-sin(Pix)Pi + ((\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)}((1 + 0)ln(\frac{1}{2}sqrt(5) + \frac{1}{2}) + \frac{(x + 1)(\frac{1}{2}*0*\frac{1}{2}*5^{\frac{1}{2}} + 0)}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})))}{ln^{2}({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})}\\=&\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}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})ln({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})} + \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}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})ln({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})} - \frac{{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}ln(\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})})ln(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})cos(Pix)}{({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})ln^{2}({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})} - \frac{(\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)}ln(\frac{1}{2}sqrt(5) + \frac{1}{2})ln(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})}{({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})ln^{2}({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})} + \frac{Pi{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}ln(-{\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{x}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})sin(Pix)}{({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})ln^{2}({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})} + \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}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{x})ln({\frac{1}{(\frac{1}{2}sqrt(5) + \frac{1}{2})}}^{(x + 1)}cos(Pix) + (\frac{1}{2}sqrt(5) + \frac{1}{2})^{(x + 1)})}\\ \end{split}\end{equation} \]
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