函数y=y(x)是由e^(x+y)+cos(xy)=0确定的,则dy/dx=?

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函数y=y(x)是由e^(x+y)+cos(xy)=0确定的,则dy/dx=?

两端对x求导得
e^(x+y)*(x+y)'-sin(xy)*(xy)'=0
e^(x+y)*(1+y')-sin(xy)*(y+y')=0
解得
dy/dx=y'=[e^(x+y)-ysin(xy)]/[sin(xy)-e^(x+y)]