Year 11 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · CalculusYear 11 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 3x3 − 3x
Answer: dy/dx = 9x2 − 3
- d/dx(3x3) = 9x2
- d/dx(−3x) = −3
2.Differentiate y = 2x3 + 2x2
Answer: dy/dx = 6x2 + 4x
- d/dx(2x3) = 6x2
- d/dx(2x2) = 4x
3.Differentiate y = 5x3 − 4x
Answer: dy/dx = 15x2 − 4
- d/dx(5x3) = 15x2
- d/dx(−4x) = −4
4.Differentiate y = −2x2 − 7x
Answer: dy/dx = −4x − 7
- d/dx(−2x2) = −4x
- d/dx(−7x) = −7
5.Differentiate y = −7x2 − 5
Answer: dy/dx = −14x
- d/dx(−7x2) = −14x
- The derivative of the constant −5 is 0
6.Differentiate y = −2x3 − 5x2
Answer: dy/dx = −6x2 − 10x
- d/dx(−2x3) = −6x2
- d/dx(−5x2) = −10x
7.Differentiate y = −6x2 − 1
Answer: dy/dx = −12x
- d/dx(−6x2) = −12x
- The derivative of the constant −1 is 0
8.Differentiate y = 7x3 − 4x2
Answer: dy/dx = 21x2 − 8x
- d/dx(7x3) = 21x2
- d/dx(−4x2) = −8x
9.Differentiate y = −x3 − x2
Answer: dy/dx = −3x2 − 2x
- d/dx(−x3) = −3x2
- d/dx(−x2) = −2x
10.Differentiate y = 2x3 + 5
Answer: dy/dx = 6x2
- d/dx(2x3) = 6x2
- The derivative of the constant 5 is 0
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