x^3+y^3-x*y=0
对x求导： 3x? + 3y?y' -y -xy' = 0 (1)
(3y?-x)y' = y - 3x?
y' = (y - 3x?)/(3y?-x) (2)
(1)两侧对x求导：6x + 6y(y')? + 3y?y" -y' -y' -xy" = 0
y" = [2y' -6x -6y(y')?]/(3y?-x) (3)
(2)(3):
y" = (54x?y? - 2xy -54yx^4 -54xy^4)/(3y?-x)^3
X+Y–XY=O 求y的二阶导数
x^3+y^3-x*y=0
对x求导： 3x? + 3y?y' -y -xy' = 0 (1)
(3y?-x)y' = y - 3x?
y' = (y - 3x?)/(3y?-x) (2)
(1)两侧对x求导：6x + 6y(y')? + 3y?y" -y' -y' -xy" = 0
y" = [2y' -6x -6y(y')?]/(3y?-x) (3)
(2)(3):
y" = (54x?y? - 2xy -54yx^4 -54xy^4)/(3y?-x)^3