1. Differentiate the function $y = 3x^2 - x^4 + 2$. Step 1: State the problem. We need to find $\frac{dy}{dx}$ for $y = 3x^2 - x^4 + 2$. Step 2: Use the power rule for differentiation: $\frac{d}{dx} x^n = nx^{n-1}$. Step 3: Differentiate each term: $$\frac{d}{dx}(3x^2) = 3 \times 2x^{2-1} = 6x$$ $$\frac{d}{dx}(-x^4) = -4x^{4-1} = -4x^3$$ $$\frac{d}{dx}(2) = 0$$ Step 4: Combine results: $$\frac{dy}{dx} = 6x - 4x^3$$ Final answer: $\boxed{6x - 4x^3}$