Question

Find $\frac{dy}{dx},if{x}^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$

Answer 1

$\left(\frac{2}{3}\right)x^{\frac{2}{3}}-1+{\frac{2}{3}}^{\frac{2}{3}}-1\frac{dy}{dx}=0$

$\Rightarrow \left(\frac{2}{3}\right)x^{\frac{-1}{3}}+\frac{2}{3}{y}^{\frac{-1}{3}}dy/dx=0$

$\Rightarrow x^{\frac{-1}{3}}+y^{\frac{-1}{3}}\frac{dy}{dx}$

$\Rightarrow \frac{dy}{dx}=-(\frac{x}{y}{)}^{\frac{-1}{3}}$

$\Rightarrow \frac{dy}{dx}=-\left(\frac{y}{x}\right)\frac{1}{3}$ ans.