1. Problem: Find $\frac{d^2y}{dx^2}$ for the function $y = 5x^2 - 7x + 3$. 2. Formula: Use the power rule $\frac{d}{dx}x^n = n x^{n-1}$ and the linearity of differentiation which allows differentiating term-by-term. 3. Important rules: The derivative of a constant is 0 and the derivative of $ax$ is $a$. 4. Intermediate work: Compute the first derivative term-by-term. $$\frac{dy}{dx} = \frac{d}{dx}(5x^2) - \frac{d}{dx}(7x) + \frac{d}{dx}(3) = 5\cdot 2 x^{1} - 7 + 0 = 10x - 7$$ 5. Compute the second derivative by differentiating the first derivative. $$\frac{d^2y}{dx^2} = \frac{d}{dx}(10x - 7) = 10$$ 6. Explanation: The term $10x$ differentiates to $10$ and the constant $-7$ differentiates to $0$, so the second derivative is constant. Final answer: $\frac{d^2y}{dx^2} = 10$.