Year 12 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · CalculusYear 12 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −7x3 − 6x
Answer: dy/dx = −21x2 − 6
- d/dx(−7x3) = −21x2
- d/dx(−6x) = −6
2.Differentiate y = −6x2 − 7
Answer: dy/dx = −12x
- d/dx(−6x2) = −12x
- The derivative of the constant −7 is 0
3.Differentiate y = 4x3 + 3x2
Answer: dy/dx = 12x2 + 6x
- d/dx(4x3) = 12x2
- d/dx(3x2) = 6x
4.Differentiate y = 6x2 − 3
Answer: dy/dx = 12x
- d/dx(6x2) = 12x
- The derivative of the constant −3 is 0
5.Differentiate y = −3x2 − 1
Answer: dy/dx = −6x
- d/dx(−3x2) = −6x
- The derivative of the constant −1 is 0
6.Differentiate y = 5x2 − 7x
Answer: dy/dx = 10x − 7
- d/dx(5x2) = 10x
- d/dx(−7x) = −7
7.Differentiate y = 4x3 − 7x
Answer: dy/dx = 12x2 − 7
- d/dx(4x3) = 12x2
- d/dx(−7x) = −7
8.Differentiate y = 8x2 + 6x
Answer: dy/dx = 16x + 6
- d/dx(8x2) = 16x
- d/dx(6x) = 6
9.Differentiate y = 3x − 6
Answer: dy/dx = 3
- d/dx(3x) = 3
- The derivative of the constant −6 is 0
10.Differentiate y = −7x2 + 8
Answer: dy/dx = −14x
- d/dx(−7x2) = −14x
- The derivative of the constant 8 is 0
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