Tangentes a gráficos de relações implícitas

Considere a curva dada pela equação $xy^2-x^3y=8$x, y, squared, minus, x, cubed, y, equals, 8. Pode ser demonstrado que $\dfrac{dy}{dx}=\dfrac{3x^2y-y^2}{2xy-x^3}$start fraction, d, y, divided by, d, x, end fraction, equals, start fraction, 3, x, squared, y, minus, y, squared, divided by, 2, x, y, minus, x, cubed, end fraction.