Year 11 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 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 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 3x4 − x3 − 5x2
Answer: dy/dx = 12x3 − 3x2 − 10x
- d/dx(3x4) = 12x3
- d/dx(−x3) = −3x2
- d/dx(−5x2) = −10x
2.Differentiate y = −4x5 − x2 − 7x
Answer: dy/dx = −20x4 − 2x − 7
- d/dx(−4x5) = −20x4
- d/dx(−x2) = −2x
- d/dx(−7x) = −7
3.Differentiate y = 6x4 + 5x3 + 5x
Answer: dy/dx = 24x3 + 15x2 + 5
- d/dx(6x4) = 24x3
- d/dx(5x3) = 15x2
- d/dx(5x) = 5
4.Differentiate y = 4x5 + 4x3 + 2
Answer: dy/dx = 20x4 + 12x2
- d/dx(4x5) = 20x4
- d/dx(4x3) = 12x2
- The derivative of the constant 2 is 0
5.Differentiate y = 8x5 − 6x2 + 6
Answer: dy/dx = 40x4 − 12x
- d/dx(8x5) = 40x4
- d/dx(−6x2) = −12x
- The derivative of the constant 6 is 0
6.Differentiate y = x4 + 6x3 + 3x2
Answer: dy/dx = 4x3 + 18x2 + 6x
- d/dx(x4) = 4x3
- d/dx(6x3) = 18x2
- d/dx(3x2) = 6x
7.Differentiate y = 2x4 + 2x3 − 3x
Answer: dy/dx = 8x3 + 6x2 − 3
- d/dx(2x4) = 8x3
- d/dx(2x3) = 6x2
- d/dx(−3x) = −3
8.Differentiate y = 2x5 + 4x3 − 6x
Answer: dy/dx = 10x4 + 12x2 − 6
- d/dx(2x5) = 10x4
- d/dx(4x3) = 12x2
- d/dx(−6x) = −6
9.Differentiate y = −3x3 − 2x2 − 1
Answer: dy/dx = −9x2 − 4x
- d/dx(−3x3) = −9x2
- d/dx(−2x2) = −4x
- The derivative of the constant −1 is 0
10.Differentiate y = −4x3 − 3x2 − 7
Answer: dy/dx = −12x2 − 6x
- d/dx(−4x3) = −12x2
- d/dx(−3x2) = −6x
- The derivative of the constant −7 is 0
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