出,我们就认为这些混合偏导数是与求导次序无关的 计算高阶偏导数,一般是用公式或逐阶计算之 习题8-2解谷 1求下列函数的偏导数 (1)z=x3y-y2x; (2) (3)z=√n(xy) (4)z=sin (ry)+cos(ry); (5)2=Intan (6)z=(1+xy); (7)=x (8u=arctan (x-y) 解(1) 3xy-y (2) U b=(a+ (3)a (In tln y)i= 2√n(xy)2x√n(xy az (In x+In y) 2√n(xy)2y√n(xy (4)=cos(xy)·y+2eos(xy)[-sin(xy)·y acos(xy)-ysin(2.xy ); =cos(xy):x+2cos(xy)·[-sin(xy)]·x rcos (ry)-xsin(2xy) x12 sec CsC 2r 2x a sec (6)=y(1+xy)·y=y2(1+xy)2;