Year 11 Differentiation (Power Rule) Worksheet — Level 2 — 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 2 — Practice Set 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 5x5 − x4 + 4x2
Answer: dy/dx = 25x4 − 4x3 + 8x
- d/dx(5x5) = 25x4
- d/dx(−x4) = −4x3
- d/dx(4x2) = 8x
2.Differentiate y = 3x5 + 2x4 − 6x
Answer: dy/dx = 15x4 + 8x3 − 6
- d/dx(3x5) = 15x4
- d/dx(2x4) = 8x3
- d/dx(−6x) = −6
3.Differentiate y = 3x5 − 2x2 − 2x
Answer: dy/dx = 15x4 − 4x − 2
- d/dx(3x5) = 15x4
- d/dx(−2x2) = −4x
- d/dx(−2x) = −2
4.Differentiate y = 6x5 + 9x4 − 4x2
Answer: dy/dx = 30x4 + 36x3 − 8x
- d/dx(6x5) = 30x4
- d/dx(9x4) = 36x3
- d/dx(−4x2) = −8x
5.Differentiate y = x5 − 5x3 + 9
Answer: dy/dx = 5x4 − 15x2
- d/dx(x5) = 5x4
- d/dx(−5x3) = −15x2
- The derivative of the constant 9 is 0
6.Differentiate y = 8x5 + 4x4 + 8
Answer: dy/dx = 40x4 + 16x3
- d/dx(8x5) = 40x4
- d/dx(4x4) = 16x3
- The derivative of the constant 8 is 0
7.Differentiate y = 6x5 − 7x3 + 5
Answer: dy/dx = 30x4 − 21x2
- d/dx(6x5) = 30x4
- d/dx(−7x3) = −21x2
- The derivative of the constant 5 is 0
8.Differentiate y = 4x5 + 9x3 − 1
Answer: dy/dx = 20x4 + 27x2
- d/dx(4x5) = 20x4
- d/dx(9x3) = 27x2
- The derivative of the constant −1 is 0
9.Differentiate y = −2x4 − 5x3 − 5
Answer: dy/dx = −8x3 − 15x2
- d/dx(−2x4) = −8x3
- d/dx(−5x3) = −15x2
- The derivative of the constant −5 is 0
10.Differentiate y = −5x5 − x2 + 1
Answer: dy/dx = −25x4 − 2x
- d/dx(−5x5) = −25x4
- d/dx(−x2) = −2x
- The derivative of the constant 1 is 0
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