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Find dy/dx. If (x² + y²)² = xy

${(x^{2} + y^{2})}^{2} = x y D i f f e r e n t i a t i n g o n b o t h s i d e s, w e h a v e, \frac{ⅆ}{ⅆ x} {(x^{2} + y^{2})}^{2} = \frac{ⅆ}{ⅆ x} (x y) \Rightarrow 2 (x^{2} + y^{2}) \frac{ⅆ}{ⅆ x} (x^{2} + y^{2}) = x \frac{ⅆ}{ⅆ x} (y) + y \frac{ⅆ}{ⅆ x} (x) \Rightarrow 2 (x^{2} + y^{2}) (\frac{ⅆ}{ⅆ x} (x^{2}) + \frac{ⅆ}{ⅆ x} (y^{2})) = x \frac{ⅆ y}{ⅆ x} + y \Rightarrow 2 (x^{2} + y^{2}) (2 x + 2 y \frac{ⅆ y}{ⅆ x}) = x \frac{ⅆ y}{ⅆ x} + y \Rightarrow 4 x^{3} + 4 x^{2} y \frac{ⅆ y}{ⅆ x} + 4 x y^{2} + 4 y^{3} \frac{ⅆ y}{ⅆ x} = x \frac{ⅆ y}{ⅆ x} + y \Rightarrow (4 x^{2} y + 4 y^{3} - x) \frac{ⅆ y}{ⅆ x} = y - 4 x^{3} - 4 x^{2} y \Rightarrow \frac{ⅆ y}{ⅆ x} = \frac{y - 4 x^{3} - 4 x^{2} y}{4 x^{2} y + 4 y^{3} - x} H e n c e, \frac{ⅆ y}{ⅆ x} = \frac{y - 4 x^{3} - 4 x^{2} y}{4 x^{2} y + 4 y^{3} - x}$

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