Question

求函数u=xsin(xyz)的全微分du.详细解答

求函数u=xsin(xyz)的全微分du???

Answer 1

先求偏导数δu/δx=sin(xyz)+xcos(xyz)*yz
δu/δy=x*2zcos(xyz)
δu/δz=x^2ycos(xyz)
所以全微分du=δu/δx*dx+δu/δydy+δu/δzdz
=(sin(xyz)+xcos(xyz)*yz)dx+x*2zcos(xyz)dy+x^2ycos(xyz)dz

Answer 2

du/dx=sin(xyz)+xyzcos(xyz)
du/dy=x^2zzcos(xyz)
du/dz=x^2yzcos(xyz)
所以du=(sin(xyz)+xyzcos(xyz))dx+(x^2zzcos(xyz))dy+(x^2yzcos(xyz))dz

Answer 3

du=[sin(xyz)+xyzcos(xyz)]dx+xxzcos（xyz)dy+xxycos(xyz)dz
平方打不上，将就看吧