Year 11 Differentiation (Power Rule) Worksheet — Level 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 6x6 − 6x5 − 3x3, find f′(−2).
Answer: f′(−2) = −1668
- d/dx(6x6) = 36x5
- d/dx(−6x5) = −30x4
- d/dx(−3x3) = −9x2
- f′(x) = 36x5 − 30x4 − 9x2
- Substitute x = −2: −1668
2.Differentiate y = 2x6 − 3x2 − 7x
Answer: dy/dx = 12x5 − 6x − 7
- d/dx(2x6) = 12x5
- d/dx(−3x2) = −6x
- d/dx(−7x) = −7
3.If f(x) = 9x6 − 3x3 + 4x2, find f′(1).
Answer: f′(1) = 53
- d/dx(9x6) = 54x5
- d/dx(−3x3) = −9x2
- d/dx(4x2) = 8x
- f′(x) = 54x5 − 9x2 + 8x
- Substitute x = 1: 53
4.If f(x) = 5x5 − 5x − 4, find f′(2).
Answer: f′(2) = 395
- d/dx(5x5) = 25x4
- d/dx(−5x) = −5
- The derivative of the constant −4 is 0
- f′(x) = 25x4 − 5
- Substitute x = 2: 395
5.Differentiate y = −2x6 − 3x4 + 6x3
Answer: dy/dx = −12x5 − 12x3 + 18x2
- d/dx(−2x6) = −12x5
- d/dx(−3x4) = −12x3
- d/dx(6x3) = 18x2
6.Differentiate y = 7x6 − 3x3 − 6
Answer: dy/dx = 42x5 − 9x2
- d/dx(7x6) = 42x5
- d/dx(−3x3) = −9x2
- The derivative of the constant −6 is 0
7.Differentiate y = 9x3 + x − 7
Answer: dy/dx = 27x2 + 1
- d/dx(9x3) = 27x2
- d/dx(x) = 1
- The derivative of the constant −7 is 0
8.Differentiate y = 6x6 + 8x2 + 6x
Answer: dy/dx = 36x5 + 16x + 6
- d/dx(6x6) = 36x5
- d/dx(8x2) = 16x
- d/dx(6x) = 6
9.If f(x) = −6x4 + 6x + 9, find f′(−2).
Answer: f′(−2) = 198
- d/dx(−6x4) = −24x3
- d/dx(6x) = 6
- The derivative of the constant 9 is 0
- f′(x) = −24x3 + 6
- Substitute x = −2: 198
10.If f(x) = x6 − 5x4 + 6x2, find f′(1).
Answer: f′(1) = −2
- d/dx(x6) = 6x5
- d/dx(−5x4) = −20x3
- d/dx(6x2) = 12x
- f′(x) = 6x5 − 20x3 + 12x
- Substitute x = 1: −2
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