用f'x表示f对x的偏导数,余者类推。
u=x^2-y^2,v=2xy,
u'x=2x,u'y=-2y,v'x=2y,v'y=2x,
z'x=z'u*u'x+z'v*v'x=2xz'u+2yz'v,
z'y=z'u*u'y+z'v*v'y=-2yz'u+2xz'v,
z''x^2=2z'u+(2x)^2*z''u^2+(2y)^2*z''v^2,
z''y^2=-2z'u+(2y)^2*z''u^2+(2x)^2*z''v^2,
∴z''x^2+z''y^2=4(x^2+y^2)(z''u^2+z''v^2)=0.