设x^2y+xy^2+2y^3=1确定y=y(x)则y的导数是?

设x^2y+xy^2+2y^3=1确定y=y(x)则y的导数是?
设x^2y+xy^2+2y^3=1确定y=y(x)则y的导数是?

设x^2y+xy^2+2y^3=1确定y=y(x)则y的导数是?

等式两边同时求导可得：(这是对于隐函数求导得一般方法)
2xy+y'*x^2+y^2+2xy*y'+6y*y'=0
--> y'= -(2xy+y^2)/(x^2+2xy+6y)
希望能帮助你哈

对x求导：
2xy+y'x^2+y^2+2yxy'+6y^2y'=0
2x+y'x^2+y+2xy'+6yy'=0