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.Differentiate y = −3x2 − 7x − 6
Answer: dy/dx = −6x − 7
- d/dx(−3x2) = −6x
- d/dx(−7x) = −7
- The derivative of the constant −6 is 0
2.If f(x) = 2x4 + 6x2 − 6x, find f′(2).
Answer: f′(2) = 82
- d/dx(2x4) = 8x3
- d/dx(6x2) = 12x
- d/dx(−6x) = −6
- f′(x) = 8x3 + 12x − 6
- Substitute x = 2: 82
3.If f(x) = 6x5 + 9x4 − 4x3, find f′(−2).
Answer: f′(−2) = 144
- d/dx(6x5) = 30x4
- d/dx(9x4) = 36x3
- d/dx(−4x3) = −12x2
- f′(x) = 30x4 + 36x3 − 12x2
- Substitute x = −2: 144
4.If f(x) = x3 − 2x2 + 7, find f′(1).
Answer: f′(1) = −1
- d/dx(x3) = 3x2
- d/dx(−2x2) = −4x
- The derivative of the constant 7 is 0
- f′(x) = 3x2 − 4x
- Substitute x = 1: −1
5.If f(x) = 7x6 + 4x + 8, find f′(1).
Answer: f′(1) = 46
- d/dx(7x6) = 42x5
- d/dx(4x) = 4
- The derivative of the constant 8 is 0
- f′(x) = 42x5 + 4
- Substitute x = 1: 46
6.Differentiate y = −5x3 + 7x2 − x
Answer: dy/dx = −15x2 + 14x − 1
- d/dx(−5x3) = −15x2
- d/dx(7x2) = 14x
- d/dx(−x) = −1
7.If f(x) = −3x6 + 8x4 − 7x, find f′(−2).
Answer: f′(−2) = 313
- d/dx(−3x6) = −18x5
- d/dx(8x4) = 32x3
- d/dx(−7x) = −7
- f′(x) = −18x5 + 32x3 − 7
- Substitute x = −2: 313
8.If f(x) = −x5 − 6x4 + 4, find f′(1).
Answer: f′(1) = −29
- d/dx(−x5) = −5x4
- d/dx(−6x4) = −24x3
- The derivative of the constant 4 is 0
- f′(x) = −5x4 − 24x3
- Substitute x = 1: −29
9.If f(x) = 3x6 − 2x3 + 4, find f′(1).
Answer: f′(1) = 12
- d/dx(3x6) = 18x5
- d/dx(−2x3) = −6x2
- The derivative of the constant 4 is 0
- f′(x) = 18x5 − 6x2
- Substitute x = 1: 12
10.Differentiate y = 3x6 + 4x3 − 4
Answer: dy/dx = 18x5 + 12x2
- d/dx(3x6) = 18x5
- d/dx(4x3) = 12x2
- The derivative of the constant −4 is 0
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