求由方程xy+sinz+y-2z=0确定的函数z=z(x，y)的全微分dz．
设F(x,y，z)=xy+sinz+y-2x，F′x=y，F′y=x+1，F′z=cosz-2，所以∂z/∂x=-(F′x/F′z)=y/(cosz-2)=y/(2-cosz),∂z/∂x=-(F′y/F′z)=(x+1)/(cosz-2)=(x+1)/(2-cosz)则dz=(∂z/∂x)dx+(∂z/∂y)dy=[y/(2-cosz)]dx+[(x+1)/(2-cosz)]dy
求由方程xy+sinz+y-2z=0确定的函数z=z(x，y)的全微分dz．
设F(x,y，z)=xy+sinz+y-2x，F′x=y，F′y=x+1，F′z=cosz-2，所以∂z/∂x=-(F′x/F′z)=y/(cosz-2)=y/(2-cosz),∂z/∂x=-(F′y/F′z)=(x+1)/(cosz-2)=(x+1)/(2-cosz)则dz=(∂z/∂x)dx+(∂z/∂y)dy=[y/(2-cosz)]dx+[(x+1)/(2-cosz)]dy
