关于多元函数微分的问题设x=(e^u)*cosv,y=(e^u)*sinv,z=uv,试求dz/dx和dz/dy(偏微分的符号不好打,用d代替了)

∵x=(e^u)*cosv,y=(e^u)*sinv,∴U=ln(x²+y²),V=arctan(y/x).∴Ux=2x/(x²+y²),Vx=-y/(x²+y²),Uy=2y/(x²+y²),Vy=x/(x²+y²).∵Z=UV,∴Zu=V,Zv=u.(Ux,Vx,Uy,Vy,Zu,Zv...