求由e^y=cos(x+y)所確定的隱函數y=y(x)的導數

求由e^y=cos(x+y)所確定的隱函數y=y(x)的導數

e^y=cos(x+y)
(e^y).y' = -sin(x+y).(1+ y')
(e^y + sin(x+y))y' = -sin(x+y)
y' =-sin(x+y)/(e^y + sin(x+y))