求由e^y=cos(x+y)所确定的隐函数y=y(x)的导数

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求由e^y=cos(x+y)所确定的隐函数y=y(x)的导数

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) )