Year 11 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −7x5 + 5x4 − 5x2
Answer: dy/dx = −35x4 + 20x3 − 10x
- d/dx(−7x5) = −35x4
- d/dx(5x4) = 20x3
- d/dx(−5x2) = −10x
2.If f(x) = 4x4 + 7x + 1, find f′(1).
Answer: f′(1) = 23
- d/dx(4x4) = 16x3
- d/dx(7x) = 7
- The derivative of the constant 1 is 0
- f′(x) = 16x3 + 7
- Substitute x = 1: 23
3.If f(x) = −6x5 + 9x + 3, find f′(−2).
Answer: f′(−2) = −471
- d/dx(−6x5) = −30x4
- d/dx(9x) = 9
- The derivative of the constant 3 is 0
- f′(x) = −30x4 + 9
- Substitute x = −2: −471
4.Differentiate y = −x6 − 7x4 − 4x
Answer: dy/dx = −6x5 − 28x3 − 4
- d/dx(−x6) = −6x5
- d/dx(−7x4) = −28x3
- d/dx(−4x) = −4
5.Differentiate y = 3x6 + 3x2 − 1
Answer: dy/dx = 18x5 + 6x
- d/dx(3x6) = 18x5
- d/dx(3x2) = 6x
- The derivative of the constant −1 is 0
6.If f(x) = −2x3 − 3x2 + 2, find f′(2).
Answer: f′(2) = −36
- d/dx(−2x3) = −6x2
- d/dx(−3x2) = −6x
- The derivative of the constant 2 is 0
- f′(x) = −6x2 − 6x
- Substitute x = 2: −36
7.Differentiate y = 2x6 + 4x5 − 5x3
Answer: dy/dx = 12x5 + 20x4 − 15x2
- d/dx(2x6) = 12x5
- d/dx(4x5) = 20x4
- d/dx(−5x3) = −15x2
8.If f(x) = −x5 + 4x3 − 4x, find f′(−2).
Answer: f′(−2) = −36
- d/dx(−x5) = −5x4
- d/dx(4x3) = 12x2
- d/dx(−4x) = −4
- f′(x) = −5x4 + 12x2 − 4
- Substitute x = −2: −36
9.If f(x) = 6x6 − 4x5 + x3, find f′(2).
Answer: f′(2) = 844
- d/dx(6x6) = 36x5
- d/dx(−4x5) = −20x4
- d/dx(x3) = 3x2
- f′(x) = 36x5 − 20x4 + 3x2
- Substitute x = 2: 844
10.Differentiate y = 6x5 − x2 − 1
Answer: dy/dx = 30x4 − 2x
- d/dx(6x5) = 30x4
- d/dx(−x2) = −2x
- The derivative of the constant −1 is 0
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