设y=y(x)是由方程ex-ey=sin(xy)所确定的隐函数，求微分dy．

设y=y(x)是由方程e^x-e^y=sin(xy)所确定的隐函数，求微分dy．
【正确答案】：在e^x-e^y=sin(xy)两边对x求导，得 e^x-e^ydy/dx=cos(xy)•(y+xdy/dx) dy/dx=e^x-ycos(xy)/e^y+xcos(xy) 即 dy=[e^x-ycos(xy)/e^y+xcos(xy)]dx．