Question

e的xy次方加xy加y等于3求导

Answer 1

e^xy+xy+y=3

那么对x求导得到

e^xy *(xy)' +(xy)' +y'=0

而

(xy)'=y+x *y'

所以

e^xy *(y+x *y') +(y+x *y') +y'=0

于是

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

得到

y'=(-y*e^xy-y) / (x*e^xy+x+1)