Use implicit differentiation to verify that \( \frac{d y}{d x} \cdot \frac{d x}{d y}=1 \), when ...

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Use implicit differentiation to verify that \( \frac{d y}{d x} \cdot \frac{d x}{d y}=1 \), when \( x^{3}+y^{3}=3 a x y \).
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