dz=df(x+1/y,y+1/x)=f1' d(x+1/y) +f2' d(y+1/x)而求全微分得到d(x+1/y)=dx -1/y^2 dy，d(y+1/x)= -1/x^2 dx+dy即dz=(1-1/x^2) dx+(1-1/y^2) dy
