Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · CalculusYear 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −3x4 + 7x3 − 7
Answer: dy/dx = −12x3 + 21x2
- d/dx(−3x4) = −12x3
- d/dx(7x3) = 21x2
- The derivative of the constant −7 is 0
2.Differentiate y = −6x3 − 2x + 4
Answer: dy/dx = −18x2 − 2
- d/dx(−6x3) = −18x2
- d/dx(−2x) = −2
- The derivative of the constant 4 is 0
3.Differentiate y = −5x4 − x + 8
Answer: dy/dx = −20x3 − 1
- d/dx(−5x4) = −20x3
- d/dx(−x) = −1
- The derivative of the constant 8 is 0
4.Differentiate y = −3x2 − 7x + 8
Answer: dy/dx = −6x − 7
- d/dx(−3x2) = −6x
- d/dx(−7x) = −7
- The derivative of the constant 8 is 0
5.Differentiate y = 5x5 + 4x + 9
Answer: dy/dx = 25x4 + 4
- d/dx(5x5) = 25x4
- d/dx(4x) = 4
- The derivative of the constant 9 is 0
6.Differentiate y = −3x5 − 7x3 − 2x
Answer: dy/dx = −15x4 − 21x2 − 2
- d/dx(−3x5) = −15x4
- d/dx(−7x3) = −21x2
- d/dx(−2x) = −2
7.Differentiate y = 9x2 + 4x + 8
Answer: dy/dx = 18x + 4
- d/dx(9x2) = 18x
- d/dx(4x) = 4
- The derivative of the constant 8 is 0
8.Differentiate y = −5x5 − 6x3 − 2x
Answer: dy/dx = −25x4 − 18x2 − 2
- d/dx(−5x5) = −25x4
- d/dx(−6x3) = −18x2
- d/dx(−2x) = −2
9.Differentiate y = 4x4 + 9x3 − 6x
Answer: dy/dx = 16x3 + 27x2 − 6
- d/dx(4x4) = 16x3
- d/dx(9x3) = 27x2
- d/dx(−6x) = −6
10.Differentiate y = 2x5 − 2x2 + 7x
Answer: dy/dx = 10x4 − 4x + 7
- d/dx(2x5) = 10x4
- d/dx(−2x2) = −4x
- d/dx(7x) = 7
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