大一高数隐函数求导

Question

如题所述

Answer 1

u=x+z v=y+z
∂F/∂u·(1+∂z/∂x)+∂F/∂v·∂z/∂x=0→∂z/∂x=-(∂F/∂u)/[(∂F/∂u)+(∂F/∂u)]
∂F/∂u·∂z/∂y+∂F/∂v·(1+∂z/∂y)=0→∂z/∂y=-(∂F/∂v)/[(∂F/∂u)+(∂F/∂u)]
dz=-(∂F/∂u)·Δx/[(∂F/∂u)+(∂F/∂u)]-(∂F/∂v)·Δy/[(∂F/∂u)+(∂F/∂u)]