If xy + yx = ab, then find dy/dx

Given xy + yx = ab
Differentiating on both sides with respect to x:

Applying the product rule of differentiation (d(uv)/dx = u(dv/dx) + v(du/dx)) to both terms on the left-hand side:

(x)(dy/dx) + (y)(1) + (y)(1) + (x)(dy/dx) = 0

x(dy/dx) + y + y + x(dy/dx) = 0

2x(dy/dx) + 2y = 0

2x(dy/dx) = -2y

dy/dx = -2y / 2x

dy/dx = -y/x