Question

FIND dy by dx of   x²+xy+y²

Answer 1

y =   x²+xy+y²
Differentiating both sides w.r.t 'x' we get,
dy/dx = 2x + y + dy/dx. x + 2y. dy/dx
 Taking all dy/dx on one side,

dy/dx - dy/dx.x - 2y. dy/dx = (2x - y)

Taking dy/dx common,
dy/dx (1-x-2y) = (2x - y)
dy/dx = (2x - y)/ (1 - x - 2y)

Answer 2

let it dy/dx=2x+y+xdy/dx+2ydy/dx dy/dx(1-x-2y)=2x+y dy/dx=2x+y/1-x-2y