Year 12 Differentiation (Power Rule) Worksheet — Level 3 — 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 3 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 6x2 − 4x + 7, find f′(1).
Answer: f′(1) = 8
- d/dx(6x2) = 12x
- d/dx(−4x) = −4
- The derivative of the constant 7 is 0
- f′(x) = 12x − 4
- Substitute x = 1: 8
2.Differentiate y = 6x5 + 4x3 − 5x2
Answer: dy/dx = 30x4 + 12x2 − 10x
- d/dx(6x5) = 30x4
- d/dx(4x3) = 12x2
- d/dx(−5x2) = −10x
3.Differentiate y = 4x6 + 8x5 + 8x2
Answer: dy/dx = 24x5 + 40x4 + 16x
- d/dx(4x6) = 24x5
- d/dx(8x5) = 40x4
- d/dx(8x2) = 16x
4.Differentiate y = 9x5 − x − 4
Answer: dy/dx = 45x4 − 1
- d/dx(9x5) = 45x4
- d/dx(−x) = −1
- The derivative of the constant −4 is 0
5.Differentiate y = 5x6 + 7x4 − 3x2
Answer: dy/dx = 30x5 + 28x3 − 6x
- d/dx(5x6) = 30x5
- d/dx(7x4) = 28x3
- d/dx(−3x2) = −6x
6.If f(x) = 3x3 + 9x2 − 2x, find f′(−1).
Answer: f′(−1) = −11
- d/dx(3x3) = 9x2
- d/dx(9x2) = 18x
- d/dx(−2x) = −2
- f′(x) = 9x2 + 18x − 2
- Substitute x = −1: −11
7.Differentiate y = −2x6 − 2x5 + 6x4
Answer: dy/dx = −12x5 − 10x4 + 24x3
- d/dx(−2x6) = −12x5
- d/dx(−2x5) = −10x4
- d/dx(6x4) = 24x3
8.Differentiate y = −3x2 + 6x + 4
Answer: dy/dx = −6x + 6
- d/dx(−3x2) = −6x
- d/dx(6x) = 6
- The derivative of the constant 4 is 0
9.If f(x) = −4x3 + 4x − 2, find f′(−2).
Answer: f′(−2) = −44
- d/dx(−4x3) = −12x2
- d/dx(4x) = 4
- The derivative of the constant −2 is 0
- f′(x) = −12x2 + 4
- Substitute x = −2: −44
10.If f(x) = 9x6 + 3x3 + x, find f′(2).
Answer: f′(2) = 1765
- d/dx(9x6) = 54x5
- d/dx(3x3) = 9x2
- d/dx(x) = 1
- f′(x) = 54x5 + 9x2 + 1
- Substitute x = 2: 1765
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.