设方程xy+sin(x+y)=1确定y是c的函数，求y´．

设方程xy+sin(x+y)=1确定y是c的函数，求y´．
【正确答案】：两边求导得：y+xy'+cos(x+y)(1+y')=0，y+cos(x+y)=-xy'-cos(x+y)•y'，∴y'=-{[y+cos(x+y)]/[x+cos(x+y)]}