计算下列隐函数的导数:cos(x+y)=xy,y'

Question

计算下列隐函数的导数:
cos(x+y)=xy,y'

Answer 1

cos(x+y)=xy两边求导得：
-(1+y')*sin(x+y)=y+xy'
-sin(x+y)-y=y'*[sin(x+y)+x]
y'=[-sin(x+y)-y]/[sin(x+y)+x]