Year 11 Differentiation (Power Rule) Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Year 11 · Mathematics · Calculus
Year 11 Differentiation (Power Rule) Worksheet — Level 2 — Answers
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Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −6x4 − 4x2 + 2
Answer: dy/dx = −24x3 − 8x
- d/dx(−6x4) = −24x3
- d/dx(−4x2) = −8x
- The derivative of the constant 2 is 0
2.Differentiate y = −6x5 − 3x2 − 7x
Answer: dy/dx = −30x4 − 6x − 7
- d/dx(−6x5) = −30x4
- d/dx(−3x2) = −6x
- d/dx(−7x) = −7
3.Differentiate y = 3x4 + 6x3 + 2
Answer: dy/dx = 12x3 + 18x2
- d/dx(3x4) = 12x3
- d/dx(6x3) = 18x2
- The derivative of the constant 2 is 0
4.Differentiate y = −x5 + x3 + x2
Answer: dy/dx = −5x4 + 3x2 + 2x
- d/dx(−x5) = −5x4
- d/dx(x3) = 3x2
- d/dx(x2) = 2x
5.Differentiate y = −x3 + 8x + 4
Answer: dy/dx = −3x2 + 8
- d/dx(−x3) = −3x2
- d/dx(8x) = 8
- The derivative of the constant 4 is 0
6.Differentiate y = −2x4 − 3x3 − 6x2
Answer: dy/dx = −8x3 − 9x2 − 12x
- d/dx(−2x4) = −8x3
- d/dx(−3x3) = −9x2
- d/dx(−6x2) = −12x
7.Differentiate y = x5 + 7x2 + 8
Answer: dy/dx = 5x4 + 14x
- d/dx(x5) = 5x4
- d/dx(7x2) = 14x
- The derivative of the constant 8 is 0
8.Differentiate y = 3x5 + 4x4 − 3x3
Answer: dy/dx = 15x4 + 16x3 − 9x2
- d/dx(3x5) = 15x4
- d/dx(4x4) = 16x3
- d/dx(−3x3) = −9x2
9.Differentiate y = 2x5 + 8x2 − 2
Answer: dy/dx = 10x4 + 16x
- d/dx(2x5) = 10x4
- d/dx(8x2) = 16x
- The derivative of the constant −2 is 0
10.Differentiate y = −3x4 − 2x3 + 7x2
Answer: dy/dx = −12x3 − 6x2 + 14x
- d/dx(−3x4) = −12x3
- d/dx(−2x3) = −6x2
- d/dx(7x2) = 14x
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