e^(xy)-(x^2)+(y^2)=1,求dy/dx
问题描述：
e^(xy)-(x^2)+(y^2)=1,求dy/dx
答
e^(xy)-(x^2)+(y^2)=1
两边同时对x求导,得
e^(xy)*(y+xy')-2x+(2yy')=0
[xe^(xy)+2y]y'=2x-ye^(xy)
dy/dx=[2x-ye^(xy)]/[xe^(xy)+2y]