1. The problem asks to find the derivative $\frac{dy}{dx}$ of the function $y = 2x^2$ using differentiation rules. 2. Recall the power rule for derivatives: if $y = x^n$, then $\frac{dy}{dx} = nx^{n-1}$. 3. Apply the power rule to $y = 2x^2$: - The constant 2 remains as a multiplier. - Differentiate $x^2$ to get $2x^{2-1} = 2x$. 4. Multiply the constant by the derivative of $x^2$: $$\frac{dy}{dx} = 2 \times 2x = 4x$$ 5. Therefore, the derivative of $y = 2x^2$ is: $$\boxed{\frac{dy}{dx} = 4x}$$ This completes the solution for the first problem in the set.