Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −x5 − x − 4
Answer: dy/dx = −5x4 − 1
- d/dx(−x5) = −5x4
- d/dx(−x) = −1
- The derivative of the constant −4 is 0
2.Differentiate y = −7x5 − 3x2 + 5x
Answer: dy/dx = −35x4 − 6x + 5
- d/dx(−7x5) = −35x4
- d/dx(−3x2) = −6x
- d/dx(5x) = 5
3.Differentiate y = 3x4 − 6x2 − 3x
Answer: dy/dx = 12x3 − 12x − 3
- d/dx(3x4) = 12x3
- d/dx(−6x2) = −12x
- d/dx(−3x) = −3
4.Differentiate y = −5x5 + 2x3 + 6x2
Answer: dy/dx = −25x4 + 6x2 + 12x
- d/dx(−5x5) = −25x4
- d/dx(2x3) = 6x2
- d/dx(6x2) = 12x
5.Differentiate y = 8x4 − 3x2 − 5x
Answer: dy/dx = 32x3 − 6x − 5
- d/dx(8x4) = 32x3
- d/dx(−3x2) = −6x
- d/dx(−5x) = −5
6.Differentiate y = x5 + 3x4 + 1
Answer: dy/dx = 5x4 + 12x3
- d/dx(x5) = 5x4
- d/dx(3x4) = 12x3
- The derivative of the constant 1 is 0
7.Differentiate y = 3x5 + 7x2 + 9x
Answer: dy/dx = 15x4 + 14x + 9
- d/dx(3x5) = 15x4
- d/dx(7x2) = 14x
- d/dx(9x) = 9
8.Differentiate y = −x4 − 6x3 − 4x2
Answer: dy/dx = −4x3 − 18x2 − 8x
- d/dx(−x4) = −4x3
- d/dx(−6x3) = −18x2
- d/dx(−4x2) = −8x
9.Differentiate y = −4x4 − 6x3 − 7
Answer: dy/dx = −16x3 − 18x2
- d/dx(−4x4) = −16x3
- d/dx(−6x3) = −18x2
- The derivative of the constant −7 is 0
10.Differentiate y = 5x2 + 9x − 1
Answer: dy/dx = 10x + 9
- d/dx(5x2) = 10x
- d/dx(9x) = 9
- The derivative of the constant −1 is 0
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