Year 11 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −4x6 − 2x2 − 4x
Answer: dy/dx = −24x5 − 4x − 4
- d/dx(−4x6) = −24x5
- d/dx(−2x2) = −4x
- d/dx(−4x) = −4
2.If f(x) = 2x5 + x4 + 6, find f′(2).
Answer: f′(2) = 192
- d/dx(2x5) = 10x4
- d/dx(x4) = 4x3
- The derivative of the constant 6 is 0
- f′(x) = 10x4 + 4x3
- Substitute x = 2: 192
3.If f(x) = 9x6 + 6x3 − 2, find f′(−2).
Answer: f′(−2) = −1656
- d/dx(9x6) = 54x5
- d/dx(6x3) = 18x2
- The derivative of the constant −2 is 0
- f′(x) = 54x5 + 18x2
- Substitute x = −2: −1656
4.Differentiate y = 3x5 − 5x2 − 6x
Answer: dy/dx = 15x4 − 10x − 6
- d/dx(3x5) = 15x4
- d/dx(−5x2) = −10x
- d/dx(−6x) = −6
5.If f(x) = 4x5 + 8x3 − 2x2, find f′(−1).
Answer: f′(−1) = 48
- d/dx(4x5) = 20x4
- d/dx(8x3) = 24x2
- d/dx(−2x2) = −4x
- f′(x) = 20x4 + 24x2 − 4x
- Substitute x = −1: 48
6.If f(x) = 3x6 − 7x4 + x3, find f′(−1).
Answer: f′(−1) = 13
- d/dx(3x6) = 18x5
- d/dx(−7x4) = −28x3
- d/dx(x3) = 3x2
- f′(x) = 18x5 − 28x3 + 3x2
- Substitute x = −1: 13
7.Differentiate y = −7x6 − 6x + 5
Answer: dy/dx = −42x5 − 6
- d/dx(−7x6) = −42x5
- d/dx(−6x) = −6
- The derivative of the constant 5 is 0
8.If f(x) = −3x5 − 5x4 − 2x2, find f′(2).
Answer: f′(2) = −408
- d/dx(−3x5) = −15x4
- d/dx(−5x4) = −20x3
- d/dx(−2x2) = −4x
- f′(x) = −15x4 − 20x3 − 4x
- Substitute x = 2: −408
9.If f(x) = −5x2 − 7x − 5, find f′(−1).
Answer: f′(−1) = 3
- d/dx(−5x2) = −10x
- d/dx(−7x) = −7
- The derivative of the constant −5 is 0
- f′(x) = −10x − 7
- Substitute x = −1: 3
10.If f(x) = −6x3 + 5x2 − 6, find f′(−2).
Answer: f′(−2) = −92
- d/dx(−6x3) = −18x2
- d/dx(5x2) = 10x
- The derivative of the constant −6 is 0
- f′(x) = −18x2 + 10x
- Substitute x = −2: −92
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