设z=xy，而x=sint,y=cos，求dz/dt．
【正确答案】：∂z/∂x=(x y)′x，=yxy-1，∂z/∂y=(xy)′y=xylnx dx/dt=(sint)′=cost，(dy/dt)=(cost)′=-sint 所以dz/dt=∂z/∂x•dx/dt+∂z/∂y•dy/dt =yxy-1•cost+xylnx•(-sint) =cos2t•(sint)cost-1-(sint)cost+1•lnsint =(sint)cost-1[cos2t-(sint)2•lnsint]
