If $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$ then $\frac{dy}{dx}$ is equal to :

$-\sqrt[3]{\frac{y}{x}}$

The correct answer is Option (1) → $-\sqrt[3]{\frac{y}{x}}$

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$

$⇒\frac{2}{3}\sqrt[3]{\frac{1}{x}}+\frac{2}{3}\sqrt[3]{\frac{1}{y}}\frac{dy}{dx}=0$

$⇒\sqrt[3]{\frac{1}{x}}=-\sqrt[3]{\frac{1}{y}}\frac{dy}{dx}$

$⇒-\left(\sqrt[3]{\frac{y}{x}}\right)=\frac{dy}{dx}$