设z=f(x,y),由F(x,y,z)=0确定,且FX(x,y,z)=a,Fy(x,y,z)=b ,Fz(x,y,z)=c,求fx的偏导

问题描述:

设z=f(x,y),由F(x,y,z)=0确定,且FX(x,y,z)=a,Fy(x,y,z)=b ,Fz(x,y,z)=c,求fx的偏导

由F(x,y,z)=0,两边对x求导得:Fx+Fz*f'x=0
所以:f'x(x,y,z)=-Fx/Fz = -a/c (c不等于0)

∂z/∂x=-Fx/Fz=-a/c