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
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)