Year 11 Differentiation (Power Rule) Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · CalculusYear 11 Differentiation (Power Rule) Worksheet — Level 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −3x3 − 4x + 1
Answer: dy/dx = −9x2 − 4
- d/dx(−3x3) = −9x2
- d/dx(−4x) = −4
- The derivative of the constant 1 is 0
2.Differentiate y = −3x4 − 2x − 5
Answer: dy/dx = −12x3 − 2
- d/dx(−3x4) = −12x3
- d/dx(−2x) = −2
- The derivative of the constant −5 is 0
3.Differentiate y = −5x5 + 2x2 − 3x
Answer: dy/dx = −25x4 + 4x − 3
- d/dx(−5x5) = −25x4
- d/dx(2x2) = 4x
- d/dx(−3x) = −3
4.Differentiate y = −x3 + x + 9
Answer: dy/dx = −3x2 + 1
- d/dx(−x3) = −3x2
- d/dx(x) = 1
- The derivative of the constant 9 is 0
5.Differentiate y = 9x4 + 8x3 − 4
Answer: dy/dx = 36x3 + 24x2
- d/dx(9x4) = 36x3
- d/dx(8x3) = 24x2
- The derivative of the constant −4 is 0
6.Differentiate y = x4 + 6x3 + 6x
Answer: dy/dx = 4x3 + 18x2 + 6
- d/dx(x4) = 4x3
- d/dx(6x3) = 18x2
- d/dx(6x) = 6
7.Differentiate y = −5x2 − 6x + 4
Answer: dy/dx = −10x − 6
- d/dx(−5x2) = −10x
- d/dx(−6x) = −6
- The derivative of the constant 4 is 0
8.Differentiate y = −5x5 + 9x4 + 9x3
Answer: dy/dx = −25x4 + 36x3 + 27x2
- d/dx(−5x5) = −25x4
- d/dx(9x4) = 36x3
- d/dx(9x3) = 27x2
9.Differentiate y = 6x5 + 6x4 + 7x
Answer: dy/dx = 30x4 + 24x3 + 7
- d/dx(6x5) = 30x4
- d/dx(6x4) = 24x3
- d/dx(7x) = 7
10.Differentiate y = −5x5 + 2x3 − 2x
Answer: dy/dx = −25x4 + 6x2 − 2
- d/dx(−5x5) = −25x4
- d/dx(2x3) = 6x2
- d/dx(−2x) = −2
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