Question

Find $\frac{dy}{dx}$ if $x^3+y^3=12xy$.

Answer 1

Given x^3+y^3=12{x}{y}

Differentiating on both sides wrt $x$

$3x^2+3y^2\frac{dy}{dx}=12(y+x\frac{dy}{dx})$

$(3y^2-12x)\frac{dy}{dx}=12y-3x^2$

$⟹\frac{dy}{dx}=\frac{12y-3x^2}{3y^2-12x}$