Question

求导：xy=x-e^xy,求dy/dx

Answer 1

答：

xy=x-e^(xy)

e^(xy)=x-xy=x(1-y)

两边对x求导：

(xy)' e^(xy)=1-y-xy'

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

ye^(xy)+xy'e^(xy)+xy'=1-y

[ 1+e^(xy) ] xy'=1-y-ye^(xy)

y'=dy/dx= [ 1-y -ye^(xy) ] / [ x+xe^(xy) ]