sin(xy)=x+y用取对数求导法怎么做

题目

sin(xy)=x+y用取对数求导法怎么做

答案

为什么要取对数呢,直接两边求导更方便啊：
sin(xy)=x+y
cos(xy)*(xy)'=1+y'
cos(xy)(y+xy')=1+y'
y'[xcos(xy)-1]=1-ycos(xy)
y'=[1-ycos(xy)]/[xcos(xy)-1].