Year 11 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = x3 − x2
Answer: dy/dx = 3x2 − 2x
- d/dx(x3) = 3x2
- d/dx(−x2) = −2x
2.Differentiate y = −5x3 − 2x
Answer: dy/dx = −15x2 − 2
- d/dx(−5x3) = −15x2
- d/dx(−2x) = −2
3.Differentiate y = 3x3 + 4x
Answer: dy/dx = 9x2 + 4
- d/dx(3x3) = 9x2
- d/dx(4x) = 4
4.Differentiate y = −7x3 + x2
Answer: dy/dx = −21x2 + 2x
- d/dx(−7x3) = −21x2
- d/dx(x2) = 2x
5.Differentiate y = −x3 + 8
Answer: dy/dx = −3x2
- d/dx(−x3) = −3x2
- The derivative of the constant 8 is 0
6.Differentiate y = 7x3 + 5x
Answer: dy/dx = 21x2 + 5
- d/dx(7x3) = 21x2
- d/dx(5x) = 5
7.Differentiate y = −2x2 − 4
Answer: dy/dx = −4x
- d/dx(−2x2) = −4x
- The derivative of the constant −4 is 0
8.Differentiate y = 7x3 − 6x
Answer: dy/dx = 21x2 − 6
- d/dx(7x3) = 21x2
- d/dx(−6x) = −6
9.Differentiate y = x3 + 6
Answer: dy/dx = 3x2
- d/dx(x3) = 3x2
- The derivative of the constant 6 is 0
10.Differentiate y = −3x3 + 3
Answer: dy/dx = −9x2
- d/dx(−3x3) = −9x2
- The derivative of the constant 3 is 0
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