Question

Find dy/dx by implicit differentiation 4x^3 + x^2y − xy^3 = 6

Answer 1

$\bf 4x^3+x^2y-xy^3=6\\\\ -------------------------------\\\\ 12x^2+\left( 2xy+x^2\cfrac{dy}{dx} \right)-\left( y^3+x3y^2\cfrac{dy}{dx} \right)=0 \\\\\\ 12x^2+2xy+x^2\cfrac{dy}{dx}-y^3-3xy^2\cfrac{dy}{dx}=0 \\\\\\ x^2\cfrac{dy}{dx}-3xy^2\cfrac{dy}{dx}=y^3-12x^2-2xy \\\\\\ \cfrac{dy}{dx}(x^2-3xy^2)=y^3-12x^2-2xy\implies \cfrac{dy}{dx}=\cfrac{y^3-12x^2-2xy}{x^2-3xy^2}$