由方程e∧y=sin(x+y)确定y为x的函数,求dy/dx.

e^y=sin(x+y)
两边求导得
e^y *y'=cos(x+y)(x+y)'=cos(x+y)(1+y')=cos(x+y)+y'cos(x+y)
[e^y-cos(x+y)]y'=cos(x+y)
y'=dy/dx=cos(x+y)/[e^y-cos(x+y)]