Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 3 — 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 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 3x5 − 3x4 + 6x3
Answer: dy/dx = 15x4 − 12x3 + 18x2
- d/dx(3x5) = 15x4
- d/dx(−3x4) = −12x3
- d/dx(6x3) = 18x2
2.Differentiate y = 6x4 + 6x2 − 2
Answer: dy/dx = 24x3 + 12x
- d/dx(6x4) = 24x3
- d/dx(6x2) = 12x
- The derivative of the constant −2 is 0
3.Differentiate y = 3x3 + 6x2 + 3
Answer: dy/dx = 9x2 + 12x
- d/dx(3x3) = 9x2
- d/dx(6x2) = 12x
- The derivative of the constant 3 is 0
4.Differentiate y = 9x3 − 4x2 − 2
Answer: dy/dx = 27x2 − 8x
- d/dx(9x3) = 27x2
- d/dx(−4x2) = −8x
- The derivative of the constant −2 is 0
5.Differentiate y = 8x5 − 6x3 − 2x2
Answer: dy/dx = 40x4 − 18x2 − 4x
- d/dx(8x5) = 40x4
- d/dx(−6x3) = −18x2
- d/dx(−2x2) = −4x
6.Differentiate y = 4x5 − 2x3 − x2
Answer: dy/dx = 20x4 − 6x2 − 2x
- d/dx(4x5) = 20x4
- d/dx(−2x3) = −6x2
- d/dx(−x2) = −2x
7.Differentiate y = −x5 + 2x4 + 6
Answer: dy/dx = −5x4 + 8x3
- d/dx(−x5) = −5x4
- d/dx(2x4) = 8x3
- The derivative of the constant 6 is 0
8.Differentiate y = 4x5 + x3 + 2x2
Answer: dy/dx = 20x4 + 3x2 + 4x
- d/dx(4x5) = 20x4
- d/dx(x3) = 3x2
- d/dx(2x2) = 4x
9.Differentiate y = 8x3 + 9x2 + 8x
Answer: dy/dx = 24x2 + 18x + 8
- d/dx(8x3) = 24x2
- d/dx(9x2) = 18x
- d/dx(8x) = 8
10.Differentiate y = −6x5 − 3x4 + 5x2
Answer: dy/dx = −30x4 − 12x3 + 10x
- d/dx(−6x5) = −30x4
- d/dx(−3x4) = −12x3
- d/dx(5x2) = 10x
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