求由方程e^y+xy+x²确定的函数y=f(x)的导数dy/dx, 求答案~谢谢好心人~

题目

求由方程e^y+xy+x²确定的函数y=f(x)的导数dy/dx, 求答案~谢谢好心人~

答案

e^y+xy+x²=C
(e^y+xy+x²)’=0
(e^y)’+(xy)+(x²)’=0
e^yy’+y+xy’+2x=0
(e^y+x)y’+y+2x=0
y’=-(y+2x)/(e^y+x)
dy/dx=-(y+2x)/(e^y+x)