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