Question

求下列方程所确定的隐函数y=f（x）的导数dy/dx

e^(x+y)-xy=1

Answer 1

两边分别对x求导有：
2x+2yy'-(y+xy')=1
2x+2yy'-y-xy'=1
(2y-x)y'=y-2x+1
dy/dx=y'=(y-2x+1)/(2y-x)