Question$1 = 3x + 2x^2y^2$ Implicit differentiation

Studdy Solution
Combine the derivatives from the previous steps:
$$0 = 3 + 4xy^2 + 4x^2y \cdot \frac{dy}{dx}$$
Solve for $\frac{dy}{dx}$:
$$0 - 3 - 4xy^2 = 4x^2y \cdot \frac{dy}{dx}$$
$$-3 - 4xy^2 = 4x^2y \cdot \frac{dy}{dx}$$
Divide both sides by $4x^2y$ to isolate $\frac{dy}{dx}$:
$$\frac{dy}{dx} = \frac{-3 - 4xy^2}{4x^2y}$$
The derivative $\frac{dy}{dx}$ is:
$$\frac{dy}{dx} = \frac{-3 - 4xy^2}{4x^2y}$$