Question

求下面隐函数的微分.y+sin(xy)=1

Answer 1

y+sin(xy)=1

两边对x求导得：y'+cos(xy)*(xy)'=0

即y'+cos(xy)*(y+xy')=0

所以y'=-ycos(xy)/(1+xcos(xy))

即dy/dx=-ycos(xy)/(1+xcos(xy))

所以dy=-ycos(xy)dx/(1+xcos(xy))

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