Year 12 Differentiation (Power Rule) Worksheet — Level 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −7x3 − 7x2 − 7
Answer: dy/dx = −21x2 − 14x
- d/dx(−7x3) = −21x2
- d/dx(−7x2) = −14x
- The derivative of the constant −7 is 0
2.Differentiate y = −x4 − 5x3 − 2x2
Answer: dy/dx = −4x3 − 15x2 − 4x
- d/dx(−x4) = −4x3
- d/dx(−5x3) = −15x2
- d/dx(−2x2) = −4x
3.Differentiate y = −2x3 − 6x + 9
Answer: dy/dx = −6x2 − 6
- d/dx(−2x3) = −6x2
- d/dx(−6x) = −6
- The derivative of the constant 9 is 0
4.Differentiate y = −3x5 − 6x4 + 6x
Answer: dy/dx = −15x4 − 24x3 + 6
- d/dx(−3x5) = −15x4
- d/dx(−6x4) = −24x3
- d/dx(6x) = 6
5.Differentiate y = 8x2 − 3x − 4
Answer: dy/dx = 16x − 3
- d/dx(8x2) = 16x
- d/dx(−3x) = −3
- The derivative of the constant −4 is 0
6.Differentiate y = −6x3 + x2 + 4
Answer: dy/dx = −18x2 + 2x
- d/dx(−6x3) = −18x2
- d/dx(x2) = 2x
- The derivative of the constant 4 is 0
7.Differentiate y = −5x4 + 9x2 − 1
Answer: dy/dx = −20x3 + 18x
- d/dx(−5x4) = −20x3
- d/dx(9x2) = 18x
- The derivative of the constant −1 is 0
8.Differentiate y = −5x5 − 5x4 − x
Answer: dy/dx = −25x4 − 20x3 − 1
- d/dx(−5x5) = −25x4
- d/dx(−5x4) = −20x3
- d/dx(−x) = −1
9.Differentiate y = 8x2 − 4x − 1
Answer: dy/dx = 16x − 4
- d/dx(8x2) = 16x
- d/dx(−4x) = −4
- The derivative of the constant −1 is 0
10.Differentiate y = −2x4 + 7x + 8
Answer: dy/dx = −8x3 + 7
- d/dx(−2x4) = −8x3
- d/dx(7x) = 7
- The derivative of the constant 8 is 0
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