Year 12 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Year 12 · Mathematics · Calculus
Year 12 Differentiation (Power Rule) Worksheet — Level 1 — Answers
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Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −7x3 + 5
Answer: dy/dx = −21x2
- d/dx(−7x3) = −21x2
- The derivative of the constant 5 is 0
2.Differentiate y = −3x3 + 6
Answer: dy/dx = −9x2
- d/dx(−3x3) = −9x2
- The derivative of the constant 6 is 0
3.Differentiate y = x2 − 6
Answer: dy/dx = 2x
- d/dx(x2) = 2x
- The derivative of the constant −6 is 0
4.Differentiate y = −3x + 7
Answer: dy/dx = −3
- d/dx(−3x) = −3
- The derivative of the constant 7 is 0
5.Differentiate y = −4x3 − 4x2
Answer: dy/dx = −12x2 − 8x
- d/dx(−4x3) = −12x2
- d/dx(−4x2) = −8x
6.Differentiate y = −4x3 + 7
Answer: dy/dx = −12x2
- d/dx(−4x3) = −12x2
- The derivative of the constant 7 is 0
7.Differentiate y = 9x3 − 3x2
Answer: dy/dx = 27x2 − 6x
- d/dx(9x3) = 27x2
- d/dx(−3x2) = −6x
8.Differentiate y = 7x + 8
Answer: dy/dx = 7
- d/dx(7x) = 7
- The derivative of the constant 8 is 0
9.Differentiate y = 3x2 − 2x
Answer: dy/dx = 6x − 2
- d/dx(3x2) = 6x
- d/dx(−2x) = −2
10.Differentiate y = −3x − 3
Answer: dy/dx = −3
- d/dx(−3x) = −3
- The derivative of the constant −3 is 0
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