Year 11 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · CalculusYear 11 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −4x5 + 3x4 + 1
Answer: dy/dx = −20x4 + 12x3
- d/dx(−4x5) = −20x4
- d/dx(3x4) = 12x3
- The derivative of the constant 1 is 0
2.Differentiate y = −3x4 + 5x3 − 2x
Answer: dy/dx = −12x3 + 15x2 − 2
- d/dx(−3x4) = −12x3
- d/dx(5x3) = 15x2
- d/dx(−2x) = −2
3.Differentiate y = 2x5 − 6x + 4
Answer: dy/dx = 10x4 − 6
- d/dx(2x5) = 10x4
- d/dx(−6x) = −6
- The derivative of the constant 4 is 0
4.Differentiate y = −x5 − 6x4 − 4
Answer: dy/dx = −5x4 − 24x3
- d/dx(−x5) = −5x4
- d/dx(−6x4) = −24x3
- The derivative of the constant −4 is 0
5.Differentiate y = 5x4 − 7x3 + 7
Answer: dy/dx = 20x3 − 21x2
- d/dx(5x4) = 20x3
- d/dx(−7x3) = −21x2
- The derivative of the constant 7 is 0
6.Differentiate y = 4x2 + 4x − 5
Answer: dy/dx = 8x + 4
- d/dx(4x2) = 8x
- d/dx(4x) = 4
- The derivative of the constant −5 is 0
7.Differentiate y = −2x5 − 7x4 + 3
Answer: dy/dx = −10x4 − 28x3
- d/dx(−2x5) = −10x4
- d/dx(−7x4) = −28x3
- The derivative of the constant 3 is 0
8.Differentiate y = x4 − x3 + 1
Answer: dy/dx = 4x3 − 3x2
- d/dx(x4) = 4x3
- d/dx(−x3) = −3x2
- The derivative of the constant 1 is 0
9.Differentiate y = 2x2 − 4x − 1
Answer: dy/dx = 4x − 4
- d/dx(2x2) = 4x
- d/dx(−4x) = −4
- The derivative of the constant −1 is 0
10.Differentiate y = −6x5 − 2x4 + 1
Answer: dy/dx = −30x4 − 8x3
- d/dx(−6x5) = −30x4
- d/dx(−2x4) = −8x3
- The derivative of the constant 1 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.