Question

求e^xy-xy=1所确定的隐函数的导数

Answer 1

两边求导：
e^(xy)*(xy)'-(xy)'=0
e^(xy)*(y+xy')-(y+xy')=0
ye^(xy)+xe^(xy)*y'=y+xy'
x(e^(xy)-1)y'=y(1-e^(xy))
y'=-y/x