求由e^(x+y)+sin(xy)=x确定的隐函数y=f(x)导数或微分

Question

如题所述

Answer 1

e^(x+y)+sin(xy)=x

(1+y')e^(x+y)+[cos(xy)](y+xy')=1

y'=-[e^(x+y)+ycos(xy)-1]/[e^(x+y)+xcos(xy)]

Answer 2

Answer 3

两边关于x求导追答

原式e^(x+y)+sin(xy)=x

求导后(1+y')e^(x+y)+[cos(xy)](y+xy')=1
整理
y'=-[e^(x+y)+ycos(xy)-1]/[e^(x+y)+xcos(xy)]