Here's an example of solving for dy/dx using implicit differentiation


y^2 + 2xy^3 - 3x^2 = 14

2y(dy/dx) + 2x(3y^2)(dy/dx) + 2y^3 - 6x = 0

2y(dy/dx) + 6xy^2(dy/dx) = 6x - 2y^3

dy/dx(2y +6xy^2) = 6x - 2y^3

dy/dx = (6x-2y^3)/(6xy^2 + 2y)

dy/dx = (3x-y^3)/(3xy^2 + y)