Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 1 derivative of a is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(({a}^{2} + {b}^{2})(d - g) + ({c}^{2} + {d}^{2})(g - b) + ({f}^{2} + {g}^{2})(d - b))}{(2a(d - g) - 2b(c - f) + 2cg - 2fd)}\ with\ respect\ to\ a：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \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}{The\ first\ derivative\ function：}\\&\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} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(({a}^{2} + {b}^{2})(d - g) + ({c}^{2} + {d}^{2})(g - b) + ({f}^{2} + {g}^{2})(d - b))}{(2a(d - g) - 2b(c - f) + 2cg - 2fd)}\ with\ respect\ to\ a：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \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}{The\ first\ derivative\ function：}\\&\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} \]