设y=y(x)是由方程e的x次方－e的y次方=sin(xy)所确定的隐函数,求微分dy

Question

如题所述

Answer 1

e^x-e^y=sin(xy)两边对x求导,把y看成复合函数：e^x-y'e^y=cos(xy)(xy)'e^x-y'e^y=cos(xy)(y+xy')e^x-ycos(xy)=y'[e^y+xcos(xy)]y'=[e^x-ycos(xy)]/[e^y+xcos(xy)]故dy=[e^x-ycos(xy)]/[e^y+xcos(xy)]dx...