Year 12 Differentiation (Power Rule) Worksheet — Level 3 — 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 8x5 + 4x4 + 8x
Answer: dy/dx = 40x4 + 16x3 + 8
- d/dx(8x5) = 40x4
- d/dx(4x4) = 16x3
- d/dx(8x) = 8
2.If f(x) = −3x5 + 7x4 + 3x2, find f′(1).
Answer: f′(1) = 19
- d/dx(−3x5) = −15x4
- d/dx(7x4) = 28x3
- d/dx(3x2) = 6x
- f′(x) = −15x4 + 28x3 + 6x
- Substitute x = 1: 19
3.Differentiate y = −4x6 + 9x2 + 3
Answer: dy/dx = −24x5 + 18x
- d/dx(−4x6) = −24x5
- d/dx(9x2) = 18x
- The derivative of the constant 3 is 0
4.If f(x) = −7x5 + 7x4 + 3x3, find f′(2).
Answer: f′(2) = −300
- d/dx(−7x5) = −35x4
- d/dx(7x4) = 28x3
- d/dx(3x3) = 9x2
- f′(x) = −35x4 + 28x3 + 9x2
- Substitute x = 2: −300
5.If f(x) = 2x6 − 5x2 + 4x, find f′(2).
Answer: f′(2) = 368
- d/dx(2x6) = 12x5
- d/dx(−5x2) = −10x
- d/dx(4x) = 4
- f′(x) = 12x5 − 10x + 4
- Substitute x = 2: 368
6.Differentiate y = x4 + 8x2 + 8
Answer: dy/dx = 4x3 + 16x
- d/dx(x4) = 4x3
- d/dx(8x2) = 16x
- The derivative of the constant 8 is 0
7.Differentiate y = 9x5 − x2 − 6x
Answer: dy/dx = 45x4 − 2x − 6
- d/dx(9x5) = 45x4
- d/dx(−x2) = −2x
- d/dx(−6x) = −6
8.If f(x) = 9x6 − 7x5 + 1, find f′(−2).
Answer: f′(−2) = −2288
- d/dx(9x6) = 54x5
- d/dx(−7x5) = −35x4
- The derivative of the constant 1 is 0
- f′(x) = 54x5 − 35x4
- Substitute x = −2: −2288
9.Differentiate y = 7x6 + 7x5 − 4x2
Answer: dy/dx = 42x5 + 35x4 − 8x
- d/dx(7x6) = 42x5
- d/dx(7x5) = 35x4
- d/dx(−4x2) = −8x
10.If f(x) = −x5 − 3x − 3, find f′(−1).
Answer: f′(−1) = −8
- d/dx(−x5) = −5x4
- d/dx(−3x) = −3
- The derivative of the constant −3 is 0
- f′(x) = −5x4 − 3
- Substitute x = −1: −8
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.