If $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$ then $\frac{dy}{dx}$ is equal to :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $-\sqrt[3]{\frac{y}{x}}$
$x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$
$⇒\frac{2}{3}\sqrt[3]{\frac{1}{x}}+\frac{2}{3}\sqrt[3]{\frac{1}{y}}\frac{dy}{dx}=0$
$⇒\sqrt[3]{\frac{1}{x}}=-\sqrt[3]{\frac{1}{y}}\frac{dy}{dx}$
$⇒-\left(\sqrt[3]{\frac{y}{x}}\right)=\frac{dy}{dx}$