设Z=Z(X,Y)是由方程Z*Z-2XYZ=1确定的隐函数,求全微分dz

设F(x,y,z)=z^2-2xyz-1
则Fx=-2yz,Fy=-2xz,Fz=2z-2xy
αz/αx=-Fx/Fz=-(-2yz)/(2z-2xy)=yz/(z-xy)
αz/αy=-Fy/Fz=xz/(z-xy)
所以
dz=αz/αx dx+αz/αy dy
=yzdx/(z-xy)+xzdy/(z-xy)