Year 12 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · CalculusYear 12 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −4x6 + 6x4 + 3x2
Answer: dy/dx = −24x5 + 24x3 + 6x
- d/dx(−4x6) = −24x5
- d/dx(6x4) = 24x3
- d/dx(3x2) = 6x
2.Differentiate y = 7x6 + 3x5 − 6x4
Answer: dy/dx = 42x5 + 15x4 − 24x3
- d/dx(7x6) = 42x5
- d/dx(3x5) = 15x4
- d/dx(−6x4) = −24x3
3.Differentiate y = 7x6 − 2x2 − 7
Answer: dy/dx = 42x5 − 4x
- d/dx(7x6) = 42x5
- d/dx(−2x2) = −4x
- The derivative of the constant −7 is 0
4.Differentiate y = −2x5 + 5x4 − 7x
Answer: dy/dx = −10x4 + 20x3 − 7
- d/dx(−2x5) = −10x4
- d/dx(5x4) = 20x3
- d/dx(−7x) = −7
5.Differentiate y = 2x4 + 7x − 3
Answer: dy/dx = 8x3 + 7
- d/dx(2x4) = 8x3
- d/dx(7x) = 7
- The derivative of the constant −3 is 0
6.If f(x) = 6x3 − x2 + 8x, find f′(2).
Answer: f′(2) = 76
- d/dx(6x3) = 18x2
- d/dx(−x2) = −2x
- d/dx(8x) = 8
- f′(x) = 18x2 − 2x + 8
- Substitute x = 2: 76
7.Differentiate y = 6x4 + 2x2 − 6x
Answer: dy/dx = 24x3 + 4x − 6
- d/dx(6x4) = 24x3
- d/dx(2x2) = 4x
- d/dx(−6x) = −6
8.If f(x) = −2x6 − x3 − 5x, find f′(2).
Answer: f′(2) = −401
- d/dx(−2x6) = −12x5
- d/dx(−x3) = −3x2
- d/dx(−5x) = −5
- f′(x) = −12x5 − 3x2 − 5
- Substitute x = 2: −401
9.Differentiate y = 2x5 − 6x3 − 1
Answer: dy/dx = 10x4 − 18x2
- d/dx(2x5) = 10x4
- d/dx(−6x3) = −18x2
- The derivative of the constant −1 is 0
10.If f(x) = −2x4 − 2x + 9, find f′(−1).
Answer: f′(−1) = 6
- d/dx(−2x4) = −8x3
- d/dx(−2x) = −2
- The derivative of the constant 9 is 0
- f′(x) = −8x3 − 2
- Substitute x = −1: 6
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.