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.Differentiate y = 2x4 + 7x + 3
Answer: dy/dx = 8x3 + 7
- d/dx(2x4) = 8x3
- d/dx(7x) = 7
- The derivative of the constant 3 is 0
2.If f(x) = 4x5 + 5x3 + 3x2, find f′(2).
Answer: f′(2) = 392
- d/dx(4x5) = 20x4
- d/dx(5x3) = 15x2
- d/dx(3x2) = 6x
- f′(x) = 20x4 + 15x2 + 6x
- Substitute x = 2: 392
3.If f(x) = −2x5 + x3 + 3x2, find f′(2).
Answer: f′(2) = −136
- d/dx(−2x5) = −10x4
- d/dx(x3) = 3x2
- d/dx(3x2) = 6x
- f′(x) = −10x4 + 3x2 + 6x
- Substitute x = 2: −136
4.If f(x) = 8x6 − x5 − x2, find f′(1).
Answer: f′(1) = 41
- d/dx(8x6) = 48x5
- d/dx(−x5) = −5x4
- d/dx(−x2) = −2x
- f′(x) = 48x5 − 5x4 − 2x
- Substitute x = 1: 41
5.If f(x) = 7x4 + 2x3 + 4x, find f′(−1).
Answer: f′(−1) = −18
- d/dx(7x4) = 28x3
- d/dx(2x3) = 6x2
- d/dx(4x) = 4
- f′(x) = 28x3 + 6x2 + 4
- Substitute x = −1: −18
6.If f(x) = 6x5 + 6x4 + 7x2, find f′(2).
Answer: f′(2) = 700
- d/dx(6x5) = 30x4
- d/dx(6x4) = 24x3
- d/dx(7x2) = 14x
- f′(x) = 30x4 + 24x3 + 14x
- Substitute x = 2: 700
7.If f(x) = −4x6 − 3x4 + 2, find f′(2).
Answer: f′(2) = −864
- d/dx(−4x6) = −24x5
- d/dx(−3x4) = −12x3
- The derivative of the constant 2 is 0
- f′(x) = −24x5 − 12x3
- Substitute x = 2: −864
8.Differentiate y = −2x3 + 7x2 + x
Answer: dy/dx = −6x2 + 14x + 1
- d/dx(−2x3) = −6x2
- d/dx(7x2) = 14x
- d/dx(x) = 1
9.If f(x) = 8x5 + 6x3 − 6, find f′(−1).
Answer: f′(−1) = 58
- d/dx(8x5) = 40x4
- d/dx(6x3) = 18x2
- The derivative of the constant −6 is 0
- f′(x) = 40x4 + 18x2
- Substitute x = −1: 58
10.If f(x) = 8x5 − 7x3 + 2x, find f′(2).
Answer: f′(2) = 558
- d/dx(8x5) = 40x4
- d/dx(−7x3) = −21x2
- d/dx(2x) = 2
- f′(x) = 40x4 − 21x2 + 2
- Substitute x = 2: 558
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