Question

微分求导X+Y-e^XY=0成立时,dY/dX怎么求 如果是X+Y+a=0呢有公式吗?

Answer 1

x+y-e^(xy)=0

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

1+y'+(1+xy')e^xy=0

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

dy/dx=y'=(-e^xy-1)/(1+xe^xy)

x+y+a=0

1+y'=0

dy/dx=y'=-1