Year 13 Differentiation (Power Rule) Worksheet — Level 3 (Set 2) — Answers
Answer sheet with worked solutions for the Year 13 calculus worksheet.
Year 13 · Mathematics · Calculus
Year 13 Differentiation (Power Rule) Worksheet — Level 3 (Set 2) — Answers
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Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −3x3 − 3x + 9
Answer: dy/dx = −9x2 − 3
- d/dx(−3x3) = −9x2
- d/dx(−3x) = −3
- The derivative of the constant 9 is 0
2.If f(x) = x6 − 7x4 + 1, find f′(−2).
Answer: f′(−2) = 32
- d/dx(x6) = 6x5
- d/dx(−7x4) = −28x3
- The derivative of the constant 1 is 0
- f′(x) = 6x5 − 28x3
- Substitute x = −2: 32
3.Differentiate y = 9x6 + 7x3 + 8x2
Answer: dy/dx = 54x5 + 21x2 + 16x
- d/dx(9x6) = 54x5
- d/dx(7x3) = 21x2
- d/dx(8x2) = 16x
4.If f(x) = −3x6 + 2x3 − 5x2, find f′(2).
Answer: f′(2) = −572
- d/dx(−3x6) = −18x5
- d/dx(2x3) = 6x2
- d/dx(−5x2) = −10x
- f′(x) = −18x5 + 6x2 − 10x
- Substitute x = 2: −572
5.Differentiate y = −5x6 + 5x4 − 4x2
Answer: dy/dx = −30x5 + 20x3 − 8x
- d/dx(−5x6) = −30x5
- d/dx(5x4) = 20x3
- d/dx(−4x2) = −8x
6.If f(x) = 2x5 + 3x + 5, find f′(2).
Answer: f′(2) = 163
- d/dx(2x5) = 10x4
- d/dx(3x) = 3
- The derivative of the constant 5 is 0
- f′(x) = 10x4 + 3
- Substitute x = 2: 163
7.Differentiate y = 8x6 − 6x5 − 5x2
Answer: dy/dx = 48x5 − 30x4 − 10x
- d/dx(8x6) = 48x5
- d/dx(−6x5) = −30x4
- d/dx(−5x2) = −10x
8.Differentiate y = −7x5 − 7x4 + x3
Answer: dy/dx = −35x4 − 28x3 + 3x2
- d/dx(−7x5) = −35x4
- d/dx(−7x4) = −28x3
- d/dx(x3) = 3x2
9.Differentiate y = −7x4 + 8x2 − 4x
Answer: dy/dx = −28x3 + 16x − 4
- d/dx(−7x4) = −28x3
- d/dx(8x2) = 16x
- d/dx(−4x) = −4
10.Differentiate y = 2x6 + x3 + 3x2
Answer: dy/dx = 12x5 + 3x2 + 6x
- d/dx(2x6) = 12x5
- d/dx(x3) = 3x2
- d/dx(3x2) = 6x
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