Find by implicit differentiation.
x²y² = 1

Verified step by step guidance

1. Start by understanding the equation: \(x^2y^2 = 1\). This is an implicit function where both \(x\) and \(y\) are variables.
2. Apply implicit differentiation to both sides of the equation with respect to \(x\). Remember that \(y\) is a function of \(x\), so when differentiating terms involving \(y\), use the chain rule.
3. Differentiate the left side: For \(x^2y^2\), use the product rule: \(\frac{d}{dx}(x^2y^2) = x^2 \cdot \frac{d}{dx}(y^2) + y^2 \cdot \frac{d}{dx}(x^2)\).
4. Continue differentiating: \(\frac{d}{dx}(y^2) = 2y \cdot \frac{dy}{dx}\) and \(\frac{d}{dx}(x^2) = 2x\). Substitute these into the product rule result.
5. Set the derivative of the right side to zero: Since the right side of the equation is a constant (1), its derivative is 0. Equate the differentiated left side to 0 and solve for \(\frac{dy}{dx}\).