对
g(x,y,z) = 0
求微分,得
(Dg/Dx)dx+(Dg/Dy)dy+(Dg/Dz)dz = 0,
可得
dz = -[(Dg/Dx)/(Dg/Dz)]dx-[(Dg/Dy)/(Dg/Dz)]dy. (*)
对
f(x-tu,y-tu,z-tu) = 0
求微分,得
f1*(dx-tdu)+f2*(dy-tdu)+f3*(dz-tdu)+ = 0,
把 (*) 代进上式,解出
du = -------- dx + -------- dy,
的形式,则
Du/Dx = ……,
Du/Dy = ……,
自然就出来了,留给你.