8-4

8-4习题841设zu2v2而uxyvxy求xzyz解xvvzxuuzxz2u12v12(uv)4xyvvzyuuzyz2u12v(1)2(uv)4y2设zu2lnv而yxuv3x2y求xzyz解xvvzxuuzxz31ln22vuyvu222)23(3)23ln(2yyxxyxyxyvvzyuuzyz)2()(ln222vuyxvu2232)23(2)23ln(2yyxxyxyx3设zex2y而xsintyt3求dtdz解dtdyyzdtdxxzdtdz2223)2(costeteyxyx)6(cos)6(cos22sin223ttettettyx4设zarcsin(xy)而x3ty4t3求dtdz解dtdyyzdtdxxzdtdz22212)(113)(11tyxyx232)43(1)41(3ttt5设zarctan(xy)而yex求dxdz解dxdyyzxzdxdzxxxexxeeyxxyxy2222221)1(116设1)(2azyeuax而yasinxzcosx求dxdu解dxdzdzudxdyyuxudxdu)sin(1cos11)(222xaexaaeazyaeaxaxax)sincoscossin(122xxaxaxaaeaxxeaxsin7设yxzarctan而xuvyuv验证22vuvuvzuz证明)()(vyyzvxxzuyyzuxxzvzuz)()(111)(11222yxyxyyx)1()()(111)(11222yxyxyyx22222vuvuyxy8求下列函数的一阶偏导数(其中f具有一阶连续偏导数)(1)uf(x2