Year 11 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Year 11 · Mathematics · Calculus
Year 11 Differentiation (Power Rule) Worksheet — Level 1 — Answers
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Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 4x2 + 2
Answer: dy/dx = 8x
- d/dx(4x2) = 8x
- The derivative of the constant 2 is 0
2.Differentiate y = −6x3 − 4x
Answer: dy/dx = −18x2 − 4
- d/dx(−6x3) = −18x2
- d/dx(−4x) = −4
3.Differentiate y = 5x3 + x2
Answer: dy/dx = 15x2 + 2x
- d/dx(5x3) = 15x2
- d/dx(x2) = 2x
4.Differentiate y = −7x + 3
Answer: dy/dx = −7
- d/dx(−7x) = −7
- The derivative of the constant 3 is 0
5.Differentiate y = x + 8
Answer: dy/dx = 1
- d/dx(x) = 1
- The derivative of the constant 8 is 0
6.Differentiate y = −5x + 3
Answer: dy/dx = −5
- d/dx(−5x) = −5
- The derivative of the constant 3 is 0
7.Differentiate y = 7x3 + 2x
Answer: dy/dx = 21x2 + 2
- d/dx(7x3) = 21x2
- d/dx(2x) = 2
8.Differentiate y = −x3 + 8x2
Answer: dy/dx = −3x2 + 16x
- d/dx(−x3) = −3x2
- d/dx(8x2) = 16x
9.Differentiate y = −x + 1
Answer: dy/dx = −1
- d/dx(−x) = −1
- The derivative of the constant 1 is 0
10.Differentiate y = −6x2 + 1
Answer: dy/dx = −12x
- d/dx(−6x2) = −12x
- The derivative of the constant 1 is 0
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