Question

求由方程xy=e^(x+y)确定的隐函数y的导函数y'

Answer 1

xy=e^(x+y)

两边对x求导得

y+xy'=e^(x+y)(1+y')

y-e^(x+y)=[e^(x+y)-x]y'

y'=[y-e^(x+y)]/[e^(x+y)-x]