Year 12 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · CalculusYear 12 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −6x3 + 4x2
Answer: dy/dx = −18x2 + 8x
- d/dx(−6x3) = −18x2
- d/dx(4x2) = 8x
2.Differentiate y = x − 6
Answer: dy/dx = 1
- d/dx(x) = 1
- The derivative of the constant −6 is 0
3.Differentiate y = 9x3 + 2x
Answer: dy/dx = 27x2 + 2
- d/dx(9x3) = 27x2
- d/dx(2x) = 2
4.Differentiate y = 9x3 − 5x2
Answer: dy/dx = 27x2 − 10x
- d/dx(9x3) = 27x2
- d/dx(−5x2) = −10x
5.Differentiate y = −2x2 + 6x
Answer: dy/dx = −4x + 6
- d/dx(−2x2) = −4x
- d/dx(6x) = 6
6.Differentiate y = 8x3 − 6x2
Answer: dy/dx = 24x2 − 12x
- d/dx(8x3) = 24x2
- d/dx(−6x2) = −12x
7.Differentiate y = −4x3 + 8x
Answer: dy/dx = −12x2 + 8
- d/dx(−4x3) = −12x2
- d/dx(8x) = 8
8.Differentiate y = 9x2 + 3x
Answer: dy/dx = 18x + 3
- d/dx(9x2) = 18x
- d/dx(3x) = 3
9.Differentiate y = −5x − 2
Answer: dy/dx = −5
- d/dx(−5x) = −5
- The derivative of the constant −2 is 0
10.Differentiate y = 9x3 + 6
Answer: dy/dx = 27x2
- d/dx(9x3) = 27x2
- The derivative of the constant 6 is 0
Marking tips
- Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
- For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
- Celebrate what went well first, then pick one thing to work on next.