z=u^v,而u=x+2y,v=x-y,求dz/dx,dz/dy。各种求过程
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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)
=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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dz/dx =dz/du *du/dx+dz/dv*dv/dx =vu^(v-1)+(u^v) lnu
dz/dy=dz/du *du/dy+dz/dv*dv/dy =2vu^(v-1)-(u^v) lnu
dz/dy=dz/du *du/dy+dz/dv*dv/dy =2vu^(v-1)-(u^v) lnu
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