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.If f(x) = 5x5 − 7x4 − x3, find f′(−1).
Answer: f′(−1) = 50
- d/dx(5x5) = 25x4
- d/dx(−7x4) = −28x3
- d/dx(−x3) = −3x2
- f′(x) = 25x4 − 28x3 − 3x2
- Substitute x = −1: 50
2.If f(x) = −x6 + 9x4 + 6x3, find f′(−2).
Answer: f′(−2) = −24
- d/dx(−x6) = −6x5
- d/dx(9x4) = 36x3
- d/dx(6x3) = 18x2
- f′(x) = −6x5 + 36x3 + 18x2
- Substitute x = −2: −24
3.Differentiate y = 7x3 − 4x + 2
Answer: dy/dx = 21x2 − 4
- d/dx(7x3) = 21x2
- d/dx(−4x) = −4
- The derivative of the constant 2 is 0
4.If f(x) = 4x4 − x2 + 2, find f′(1).
Answer: f′(1) = 14
- d/dx(4x4) = 16x3
- d/dx(−x2) = −2x
- The derivative of the constant 2 is 0
- f′(x) = 16x3 − 2x
- Substitute x = 1: 14
5.Differentiate y = 6x6 + 3x5 + 4x
Answer: dy/dx = 36x5 + 15x4 + 4
- d/dx(6x6) = 36x5
- d/dx(3x5) = 15x4
- d/dx(4x) = 4
6.If f(x) = −6x3 + 7x2 − 4x, find f′(1).
Answer: f′(1) = −8
- d/dx(−6x3) = −18x2
- d/dx(7x2) = 14x
- d/dx(−4x) = −4
- f′(x) = −18x2 + 14x − 4
- Substitute x = 1: −8
7.Differentiate y = −2x4 + 9x + 2
Answer: dy/dx = −8x3 + 9
- d/dx(−2x4) = −8x3
- d/dx(9x) = 9
- The derivative of the constant 2 is 0
8.If f(x) = 7x3 + 7x2 + 5x, find f′(1).
Answer: f′(1) = 40
- d/dx(7x3) = 21x2
- d/dx(7x2) = 14x
- d/dx(5x) = 5
- f′(x) = 21x2 + 14x + 5
- Substitute x = 1: 40
9.Differentiate y = −2x5 + 9x3 + 4
Answer: dy/dx = −10x4 + 27x2
- d/dx(−2x5) = −10x4
- d/dx(9x3) = 27x2
- The derivative of the constant 4 is 0
10.If f(x) = 9x4 − 4x3 + 5, find f′(2).
Answer: f′(2) = 240
- d/dx(9x4) = 36x3
- d/dx(−4x3) = −12x2
- The derivative of the constant 5 is 0
- f′(x) = 36x3 − 12x2
- Substitute x = 2: 240
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