Find the derivative (dy)/(dx) of the curve x² + x²y = 12.

Step 1: Find the derivative $\frac{dy}{dx}$ of the curve $x^2 + x^2y = 12$.
The equation of the curve is $x^2 + x^2y = 12$.
Differentiate both sides with respect to $x$:

$$\frac{d}{dx}(x^2) + \frac{d}{dx}(x^2y) = \frac{d}{dx}(12)$$

Using the product rule for $x^2y$:

$$2x + (2xy + x^2\frac{dy}{dx}) = 0$$ $$2x + 2xy + x^2\frac{dy}{dx} = 0$$

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