1. Stating the problem: Differentiate the function $y=(2x-1)(4x+3)$ with respect to $x$. 2. Use the product rule for differentiation: If $y = u \, v$, then $\frac{dy}{dx} = u'v + uv'$. 3. Identify $u=2x-1$ and $v=4x+3$. 4. Differentiate both functions individually: $$u' = \frac{d}{dx}(2x-1) = 2$$ $$v' = \frac{d}{dx}(4x+3) = 4$$ 5. Apply the product rule: $$\frac{dy}{dx} = u'v + uv' = 2(4x+3) + (2x-1)4$$ 6. Simplify each term: $$2(4x+3) = 8x + 6$$ $$(2x-1)4 = 8x - 4$$ 7. Add the terms: $$8x + 6 + 8x - 4 = (8x + 8x) + (6 - 4) = 16x + 2$$ Final answer: $$\frac{dy}{dx} = 16x + 2$$