求由方程x^2+2xy-y^2=2x,所确定的隐函数y=y(x)的导数dy/dx

问题描述:

求由方程x^2+2xy-y^2=2x,所确定的隐函数y=y(x)的导数dy/dx

2x + 2y + 2xy' -2yy'=2
y'(x-y)=1-x-y
dy/dx = (1-x-y)/(x-y)