xy=e^(x+y),求dy/dx.为什么不可以在两边求对数,而要直接对原函数两边光宇x求导

已知xy=e^(x+y),求dy/dx.解一：将原式写成F(x,y)=xy-e^(x+y)=0则dy/dx=-(∂F/∂x)/(∂F/∂y)=-[y-e^(x+y)]/[x-e^(x+y)]=-(y-xy)/(x-xy)=(xy-y)/(x-xy)；解二：直接求导：y+xy′=[e^(x+y)](1+y′...