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 a 求 1 阶导数。
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(({a}^{2} + {b}^{2})(d - g) + ({c}^{2} + {d}^{2})(g - b) + ({f}^{2} + {g}^{2})(d - b))}{(2a(d - g) - 2b(c - f) + 2cg - 2fd)} 关于 a 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{da^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{ga^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{b^{2}d}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{b^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{gc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{d^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bd^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{df^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{dg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{da^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{ga^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{b^{2}d}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{b^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{gc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{d^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bd^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{df^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{dg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)}\right)}{da}\\=&(\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})da^{2} + \frac{d*2a}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})ga^{2} - \frac{g*2a}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})b^{2}d + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})b^{2}g + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})gc^{2} + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bc^{2} + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})d^{2}g + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bd^{2} + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})df^{2} + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bf^{2} + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})dg^{2} + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bg^{2} + 0\\=&\frac{-2d^{2}a^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{4dga^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2da}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{2g^{2}a^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2ga}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{4b^{2}dg}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bdc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bgc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2dgc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2g^{2}c^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bd^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bgf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2dgf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bdf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bdg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2d^{2}f^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2d^{3}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bd^{3}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2b^{2}g^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2dg^{3}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2b^{2}d^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bg^{3}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}}\\ \end{split}\end{equation} \]
注意，变量是区分大小写的。
\[ \begin{equation}\begin{split}【1/1】求函数\frac{(({a}^{2} + {b}^{2})(d - g) + ({c}^{2} + {d}^{2})(g - b) + ({f}^{2} + {g}^{2})(d - b))}{(2a(d - g) - 2b(c - f) + 2cg - 2fd)} 关于 a 的 1 阶导数：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\解:&\\ &原函数 = \frac{da^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{ga^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{b^{2}d}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{b^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{gc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{d^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bd^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{df^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{dg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)}\\&\color{blue}{函数的第 1 阶导数：}\\&\frac{d\left( \frac{da^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{ga^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{b^{2}d}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{b^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{gc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{d^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bd^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{df^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{dg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{bg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)}\right)}{da}\\=&(\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})da^{2} + \frac{d*2a}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})ga^{2} - \frac{g*2a}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})b^{2}d + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})b^{2}g + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})gc^{2} + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bc^{2} + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})d^{2}g + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bd^{2} + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})df^{2} + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bf^{2} + 0 + (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})dg^{2} + 0 - (\frac{-(2d - 2g + 0 + 0 + 0 + 0)}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}})bg^{2} + 0\\=&\frac{-2d^{2}a^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{4dga^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2da}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} - \frac{2g^{2}a^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2ga}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)} + \frac{4b^{2}dg}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bdc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bgc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2dgc^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2g^{2}c^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bd^{2}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bgf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2dgf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bdf^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bdg^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2d^{2}f^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2d^{3}g}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2bd^{3}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2b^{2}g^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} + \frac{2dg^{3}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2b^{2}d^{2}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}} - \frac{2bg^{3}}{(2da - 2ga - 2bc + 2bf + 2gc - 2df)^{2}}\\ \end{split}\end{equation} \]
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