设z=u^2+v^2,u= x+ y,v=x-y,求dz

问题描述:

设z=u^2+v^2,u= x+ y,v=x-y,求dz

z'x=z'u*u'x+z'v*v'x
=2u+2v
z'y=z'u*u'y+z'v*v'y
=2u-2v
dz=z'xdx+z'ydy
=(2u+2v)dx+(2u-2v)dy