Differentiating both sides of
[tex]x^3-y^3=1[/tex]
with respect to x yields (using the chain rule)
[tex]3x^2 - 3y^2 \dfrac{\mathrm dy}{\mathrm dx} = 0[/tex]
Solve for dy/dx :
[tex]3x^2 - 3y^2 \dfrac{\mathrm dy}{\mathrm dx} = 0 \\\\ 3y^2\dfrac{\mathrm dy}{\mathrm dx} = 3x^2 \\\\ \dfrac{\mathrm dy}{\mathrm dx} = \dfrac{3x^2}{3y^2} = \dfrac{x^2}{y^2}[/tex]
The answer is then D.
