设z=f(x,y)满足x²+2y²+3z²+xy-z-9=0,求z对x的二阶偏导数.

设z=f(x,y)满足x²+2y²+3z²+xy-z-9=0,求z对x的二阶偏导数.
设z=f(x,y)满足x²+2y²+3z²+xy-z-9=0,求z对x的二阶偏导数.

设z=f(x,y)满足x²+2y²+3z²+xy-z-9=0,求z对x的二阶偏导数.
2x+6z ∂z/∂x +y-∂z/∂x=0
∴(6z-1)∂z/∂x=-2x-y
∂z/∂x=(2x+y)/(1-6z)
∂²z/∂x²= [2(1-6z) -(2x+y) (-6∂z/∂x)]/(1-6z)²
=[2(1-6z)+6(2x+y)×(2x+y)/(1-6z)]/(1-6z)²
=2/(1-6z) +6(2x+y)²/(1-6z)³