z=u^v,而u=x+2y,v=x-y,求dz/dx,dz/dy.各种求过程

问题描述:

z=u^v,而u=x+2y,v=x-y,求dz/dx,dz/dy.各种求过程
1个回答 分类:数学 2014-11-25

问题解答:

我来补答
dz/dx
=dz/du*du/dx+dz/dv*dv/dx
=vu^(v-1)+u^vlnu
=(x-y)(x+2y)^(x-y-1)+(x+2y)^(x-y)ln(x+2y)
dz/dy
=dz/du*du/dy+dz/dv*dv/dy
=2vu^(v-1)-u^vlnu
=2(x-y)(x+2y)^(x-y-1)-(x+2y)^(x-y)ln(x+2y)
 
 
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