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。
\[ \begin{equation}\begin{split}【1/1】求函数{(\frac{(Asin(x) - B)}{({A}^{2}{cos(x)}^{2} + {(A - Bsin(x))}^{2})})}^{2} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{A^{2}sin^{2}(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - \frac{2ABsin(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + \frac{B^{2}}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{A^{2}sin^{2}(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - \frac{2ABsin(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + \frac{B^{2}}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}}\right)}{dx}\\=&(\frac{-2(A^{2}*-2cos(x)sin(x) - 2ABcos(x) + 0 + B^{2}*2sin(x)cos(x))}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}})A^{2}sin^{2}(x) + \frac{A^{2}*2sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - 2(\frac{-2(A^{2}*-2cos(x)sin(x) - 2ABcos(x) + 0 + B^{2}*2sin(x)cos(x))}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}})ABsin(x) - \frac{2ABcos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + (\frac{-2(A^{2}*-2cos(x)sin(x) - 2ABcos(x) + 0 + B^{2}*2sin(x)cos(x))}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}})B^{2} + 0\\=&\frac{4A^{4}sin^{3}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{4A^{3}Bsin^{2}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{4A^{2}B^{2}sin^{3}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} + \frac{2A^{2}sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - \frac{4A^{2}B^{2}sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} + \frac{8AB^{3}sin^{2}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{2ABcos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + \frac{4AB^{3}cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{4B^{4}sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数{(\frac{(Asin(x) - B)}{({A}^{2}{cos(x)}^{2} + {(A - Bsin(x))}^{2})})}^{2} 关于 x 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{A^{2}sin^{2}(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - \frac{2ABsin(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + \frac{B^{2}}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{A^{2}sin^{2}(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - \frac{2ABsin(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + \frac{B^{2}}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}}\right)}{dx}\\=&(\frac{-2(A^{2}*-2cos(x)sin(x) - 2ABcos(x) + 0 + B^{2}*2sin(x)cos(x))}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}})A^{2}sin^{2}(x) + \frac{A^{2}*2sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - 2(\frac{-2(A^{2}*-2cos(x)sin(x) - 2ABcos(x) + 0 + B^{2}*2sin(x)cos(x))}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}})ABsin(x) - \frac{2ABcos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + (\frac{-2(A^{2}*-2cos(x)sin(x) - 2ABcos(x) + 0 + B^{2}*2sin(x)cos(x))}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}})B^{2} + 0\\=&\frac{4A^{4}sin^{3}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{4A^{3}Bsin^{2}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{4A^{2}B^{2}sin^{3}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} + \frac{2A^{2}sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} - \frac{4A^{2}B^{2}sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} + \frac{8AB^{3}sin^{2}(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{2ABcos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{2}} + \frac{4AB^{3}cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}} - \frac{4B^{4}sin(x)cos(x)}{(A^{2}cos^{2}(x) - 2ABsin(x) + A^{2} + B^{2}sin^{2}(x))^{3}}\\ \end{split}\end{equation} \]
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