设x^2-2y^3+z^2-4z=0,求δz/δx,δz/δy

Question

设x^2-2y^3+z^2-4z=0,求δz/δx,δz/δy

Answer 1

两边取全微分
2xdx-6y^2dy+(2z-4)dz=0
所以dz=[x/(2-z)]dx+[3y^2/(z-2)]dy
所以z'x=x/(2-z),z'y=3y^2/(z-2)