Find $\frac{dy}{dx}$ if (x² + y²)² = xy.

Solution

${(x^{2} + y^{2})}^{2} = xy . . . . . . . . . . . . (i)$

Differentiating with respect to x, we have,

$2 (x^{2} + y^{2}) (2 x + 2 y \frac{dy}{dx}) = x \frac{dy}{dx} + y \Rightarrow (2 x^{2} + 2 y^{2}) (2 x + 2 y \frac{dy}{dx}) = x \frac{dy}{dx} + y \Rightarrow 4 x^{3} + 4 x^{2} y \frac{dy}{dx} + 4 {xy}^{2} + 4 y^{3} \frac{dy}{dx} = x \frac{dy}{dx} + y \Rightarrow 4 x^{2} y \frac{dy}{dx} + 4 y^{3} \frac{dy}{dx} - x \frac{dy}{dx} = y - 4 x^{3} - 4 {xy}^{2} \Rightarrow (4 x^{2} y + 4 y^{3} - x) \frac{dy}{dx} = y - 4 x^{3} - 4 {xy}^{2} \Rightarrow \frac{dy}{dx} = \frac{y - 4 x^{3} - 4 {xy}^{2}}{4 x^{2} y + 4 y^{3} - x}$

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Continuity And Differentiability

Find dydx if (x2 + y2)2 = xy.

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find $\frac{dy}{dx}$ if (x² + y²)² = xy.