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由x^3+y^3+z^3-3xyz=0,得x=-1,y=0时z=1.
3x^2dx+3y^2dy+3z^2dz-3yzdx-3xzdy-3xydz=0,
(z^2-xy)dz=(yz-x^2)dx+(xz-y^2)dy,
dz=[(yz-x^2)dx+(xz-y^2)dy]/(z^2-xy),
由u=x^2*e^y*z^3得
du=2xe^y*z^3dx+x^2*e^y*z^3dy+3x^2*e^y*z^2dz
=2xe^y*z^3dx+x^2*e^y*z^3dy+3x^2*e^y*z^2*[(yz-x^2)dx+(xz-y^2)dy]/(z^2-xy),
∴du|x=-1,y=0,z=1
=-2dx+dy+3(-dx-dy)
=-5dx-2dy.
3x^2dx+3y^2dy+3z^2dz-3yzdx-3xzdy-3xydz=0,
(z^2-xy)dz=(yz-x^2)dx+(xz-y^2)dy,
dz=[(yz-x^2)dx+(xz-y^2)dy]/(z^2-xy),
由u=x^2*e^y*z^3得
du=2xe^y*z^3dx+x^2*e^y*z^3dy+3x^2*e^y*z^2dz
=2xe^y*z^3dx+x^2*e^y*z^3dy+3x^2*e^y*z^2*[(yz-x^2)dx+(xz-y^2)dy]/(z^2-xy),
∴du|x=-1,y=0,z=1
=-2dx+dy+3(-dx-dy)
=-5dx-2dy.
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