Find frac{dy}{dx},if x^{frac{2}{3}} + y^{frac | vedclass

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Question

(A) Given equation: $x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$.Differentiating both sides with respect to $x$:$\frac{d}{dx}(x^{\frac{2}{3}}

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Given equation: $x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$.Differentiating both sides with respect to $x$:$\frac{d}{dx}(x^{\frac{2}{3}}) + \frac{d}{dx}(y^{\frac{2}{3}}) = \frac{d}{dx}(a^{\frac{2}{3}})$Using the chain rule:$\frac{2}{3}x^{-\frac{1}{3}} + \frac{2}{3}y^{-\frac{1}{3}} \cdot \frac{dy}{dx} = 0$$\frac{2}{3}y^{-\frac{1}{3}} \cdot \frac{dy}{dx} = -\frac{2}{3}x^{-\frac{1}{3}}$$\frac{dy}{dx} = -\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$$\frac{dy}{dx} = -\left(\frac{y}{x}\right)^{\frac{1}{3}} = -\sqrt[3]{\frac{y}{x}}$

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

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