Differentiate y = 3x².

**The reasoning** When differentiating, we use the **power rule**: bring down the exponent as a coefficient, then reduce the exponent by 1. For y = 3x²: - The coefficient is 3 - The exponent is 2 - Bring down the 2: 3 × 2 = 6 - Reduce the exponent: 2 − 1 = 1 - Result: 6x¹ = **6x** The formula is: if y = axⁿ, then dy/dx = n·axⁿ⁻¹ **Why the wrong options tempt you** **A) 3x** — You forgot to multiply by the original exponent (2). You only reduced the power but didn't bring down the 2. **C) x³** — You *integrated* instead of differentiated! Integration raises the power; differentiation lowers it. **D) 6** — You differentiated twice by accident, or forgot that x¹ = x (you can't just drop the variable). **Quick takeaway** Power rule: **multiply by the exponent, then subtract 1 from the exponent** — always do both steps, and keep your variable unless it disappears naturally (like x⁰ = 1).