Differentiate (3x² + 2x - 5) with respect to x.

**The reasoning** We're using the **power rule of differentiation**: when you differentiate xⁿ, you get n·xⁿ⁻¹. Let's break down (3x² + 2x - 5) term by term: - **3x²**: Bring down the power 2, multiply by 3 → 2 × 3x²⁻¹ = **6x** - **2x**: This is really 2x¹, so bring down the 1 → 1 × 2x⁰ = **2** (since x⁰ = 1) - **-5**: This is a constant. Constants vanish when differentiated → **0** Add them up: 6x + 2 + 0 = **6x + 2** **Why the wrong options tempt you** - **B (3x + 2)**: You forgot to multiply by the power when differentiating 3x². Easy slip! - **C (6x - 5)**: You differentiated 2x wrongly (maybe got confused) and kept the constant -5 instead of removing it. - **D (6x + 2 - 5)**: You kept the constant! Remember: constants always disappear during differentiation because their rate of change is zero. **Quick takeaway** When differentiating polynomials, bring down powers and reduce them by 1; constants always vanish because they don't change.