隐函数的求导

1、xyz^2 = x^2 + y^3；两边对x取偏导，yz^2 +2xyz *∂z/∂x = 2x2xyz *∂z/∂x = 2x - yz^2∂z/∂x = (2x - yz^2 )/2xyz；两边对y取偏导，xz^2 +2xyz *∂z/∂x = 3y22xyz *∂z/∂x = 3y2 - xz^2∂z/∂x = ( 3y2 - xz^2 )/2xyz；2、e^z - xyz = 0对x取偏导，e^z *∂z/∂x- yz - xy *∂z/∂x = 0( e^z -xy ) *∂z/∂x = yz∂z/∂x =yz/( e^z -xy )∂²z/∂x²= { y *∂z/∂x*( e^z -xy ) - yz[e^z*∂z/∂x - y ] }/( e^z -xy )^2={ y *yz/( e^z -xy )*( e^z -xy ) - yz[e^z*yz/( e^z -xy )- y ] }/( e^z -xy )^2={ y^2z + y^2z - y^2z^2e^z/( e^z -xy ) }/( e^z -xy )^2={ ( y^2z + y^2z )( e^z -xy )- y^2z^2e^z }/( e^z -xy )^3=y^2z{ 2e^z - 2xy - ze^z }/( e^z -xy )^3=y^2z{ ( 2 - z )e^z - 2xy }/( e^z -xy )^3