Year 11 Differentiation (Power Rule) Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 5x5 − 7x2 + 2x, find f′(−1).
Answer: f′(−1) = 41
- d/dx(5x5) = 25x4
- d/dx(−7x2) = −14x
- d/dx(2x) = 2
- f′(x) = 25x4 − 14x + 2
- Substitute x = −1: 41
2.Differentiate y = −3x6 − x4 − 2x
Answer: dy/dx = −18x5 − 4x3 − 2
- d/dx(−3x6) = −18x5
- d/dx(−x4) = −4x3
- d/dx(−2x) = −2
3.Differentiate y = 7x6 + 3x4 + 4
Answer: dy/dx = 42x5 + 12x3
- d/dx(7x6) = 42x5
- d/dx(3x4) = 12x3
- The derivative of the constant 4 is 0
4.If f(x) = 5x3 + 3x2 − 6, find f′(−1).
Answer: f′(−1) = 9
- d/dx(5x3) = 15x2
- d/dx(3x2) = 6x
- The derivative of the constant −6 is 0
- f′(x) = 15x2 + 6x
- Substitute x = −1: 9
5.If f(x) = −2x6 − 4x2 − 4, find f′(−1).
Answer: f′(−1) = 20
- d/dx(−2x6) = −12x5
- d/dx(−4x2) = −8x
- The derivative of the constant −4 is 0
- f′(x) = −12x5 − 8x
- Substitute x = −1: 20
6.Differentiate y = −7x5 − x4 + 6x2
Answer: dy/dx = −35x4 − 4x3 + 12x
- d/dx(−7x5) = −35x4
- d/dx(−x4) = −4x3
- d/dx(6x2) = 12x
7.Differentiate y = −2x6 + 5x + 6
Answer: dy/dx = −12x5 + 5
- d/dx(−2x6) = −12x5
- d/dx(5x) = 5
- The derivative of the constant 6 is 0
8.If f(x) = x6 + 9x5 + 8x, find f′(1).
Answer: f′(1) = 59
- d/dx(x6) = 6x5
- d/dx(9x5) = 45x4
- d/dx(8x) = 8
- f′(x) = 6x5 + 45x4 + 8
- Substitute x = 1: 59
9.Differentiate y = 4x4 + 8x2 − 2
Answer: dy/dx = 16x3 + 16x
- d/dx(4x4) = 16x3
- d/dx(8x2) = 16x
- The derivative of the constant −2 is 0
10.Differentiate y = −5x4 + 9x3 + 7
Answer: dy/dx = −20x3 + 27x2
- d/dx(−5x4) = −20x3
- d/dx(9x3) = 27x2
- The derivative of the constant 7 is 0
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