Question

How do you differentiate `(y+x)^2+2y-x=0`?

Answer 1

If `(y + x)^2 +2y - x = 0`:

`y^2 + 2xy + x^2 + 2y -x = 0`

`2y(dy/dx) + 2(y + x(dy/dx)) + 2x + 2(dy/dx) - 1 = 0`

`2y(dy/dx) + 2y + 2x(dy/dx) + 2x + 2(dy/dx) - 1= 0`

`2y(dy/dx) + 2x(dy/dx) + 2(dy/dx) = 1 - 2x - 2y`

`dy/dx(2y + 2x + 2) = (1 - 2x- 2y)`

`dy/dx = (1- 2x - 2y)/(2y + 2x + 2)`

Hopefully this helps!