求有方程y=x+ln y所确定的函数y=y(x)的微分dy

F(x,y)=x+lny-y=0dF(x,y)=0=(∂F(x,y)dx/∂x)+(∂F(x,y)dy/∂y) dy/dx=-(∂F(x,y)/∂x)/(∂F(x,y)/∂y) =-1/(1/y-1)=y/(y-1)dy=ydx/(y-1)