设z=z(x,y)是由方程x눀+ y눀+ z눀=xyz 确定的函数,求dz

2025-06-22 01:15:43
推荐回答(1个)
回答1:

F=x^2 +y^2 +z^2-xyz,

Fx=2x-yz, Fy=2y-xz, Fz=2z-xy,
∂z/∂x=-Fx/fz=-(2x-yz)/(2z-xy),
∂z/∂y=-Fy/fz=-(2y-xz)/(2z-xy),
dz=-(2x-yz)/(2z-xy)•dx-(2y-xz)/(2z-xy)•dy.