设函数z=u^2+v^2,其中u=x+y,v=x-y,求δz⼀δx,δz⼀δy

2025-04-14 17:15:44
推荐回答(1个)
回答1:

先求u'(x)=1,u'(y)=1, v'(x)=1,v'(y)=-1,
再求z'(x),z'(y)
(1)z对x求导: δz/δx=z'(x)=2uu'(x)+2vv'(x)=2u*1+2v*1=2(x+y)+2(x-y)=4x
(2)z对y求导: δz/δy=z'(y)=2uu'(y)+2vv'(y)=2u*1+2v*(-1)=2(x+y)-2(x-y)=4y