求下列函数的偏导数：
(1)z=x3y-xy3；
(2)z=3/y2-1/3√x+ln5；
(3)z=xe-xy；
(4)z=(x+y)/(x-y)；
(5)z=arctan(y/x)；
(6)z=sin(xy)+cos2(xy)；
(7)u=sin(x2+y2+z2)；
(8)u=xy/z．
(1) ∂z/∂x=3x2y-y3，z/y=x3-3xy2 (2) ∂z/∂x=(1/3)x-(4/3)，z/y=-(6/y3) (3) ∂z/∂x=e-xy(1-xy),z/y=-x2e-xy (4) ∂z/∂x=[(x-y)-(x+y)]/(x-y)2=-2y(x-y)2 ∂z/∂y=[(x-y)+(x+y)]/(x-y)2=2x/(x-y)2 (5) ∂z/∂x=-(y/x2)/[1+(y/x)2]=-y/(x2+y2), ∂z/∂y=(1/x)/[1+(y/x)]2=x/(x2+y2) (6) ∂z/∂x=ycos(xy)+2cos(xy)[-sin(xy)]•y =ycos(xy)[1-2sin(xy)] ∂z/∂y=xcos(xy)+2cos(xy)[-sin(xy)]•x =xcos(xy)[1-2sin(xy)] (7) ∂u/∂x=cos(x2+y2+z2)•2x=2xcos(x2+y2+z2) ∂u/∂y=cos(x2+y2+z2)•2y=2ycos(x2+y2+z2) ∂u/∂z=c0s(x2+y2+z2)•2z=2zcos(x2+y2+z2) (8) ∂u/∂x=(y/z)x(y/z)-1，u/y=xy/z•lnx=(1/z)xy/zlnx ∂u/∂y=xy/z •lnx•[-(y/z2)]=-(y/z2)xy/zlnx
