Question

If $x^3+y^3=3axy$, find $\frac{dy}{dx}$.

Answer 1

$x^3+y^3=3axy$

Differentiating w.r.t. x, we get,

$\Rightarrow 3x^2+3y^2\frac{dy}{dx}=3a[x\frac{dy}{dx}+y]$

$\Rightarrow 3x^2+3y^2\frac{dy}{dx}=3ax\frac{dy}{dx}+3ay$

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

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

$\Rightarrow \frac{dy}{dx}=\frac{ay-x^2}{y^2-ax}$