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