Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · CalculusYear 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −x5 − 3x + 2
Answer: dy/dx = −5x4 − 3
- d/dx(−x5) = −5x4
- d/dx(−3x) = −3
- The derivative of the constant 2 is 0
2.Differentiate y = 5x5 − 2x3 − x
Answer: dy/dx = 25x4 − 6x2 − 1
- d/dx(5x5) = 25x4
- d/dx(−2x3) = −6x2
- d/dx(−x) = −1
3.Differentiate y = 8x5 − 5x3 + 9x
Answer: dy/dx = 40x4 − 15x2 + 9
- d/dx(8x5) = 40x4
- d/dx(−5x3) = −15x2
- d/dx(9x) = 9
4.Differentiate y = −4x5 + 4x2 − 3
Answer: dy/dx = −20x4 + 8x
- d/dx(−4x5) = −20x4
- d/dx(4x2) = 8x
- The derivative of the constant −3 is 0
5.Differentiate y = 8x5 − 6x3 − 5
Answer: dy/dx = 40x4 − 18x2
- d/dx(8x5) = 40x4
- d/dx(−6x3) = −18x2
- The derivative of the constant −5 is 0
6.Differentiate y = 8x4 − 7x3 − 3x
Answer: dy/dx = 32x3 − 21x2 − 3
- d/dx(8x4) = 32x3
- d/dx(−7x3) = −21x2
- d/dx(−3x) = −3
7.Differentiate y = 2x3 − 2x2 − 6x
Answer: dy/dx = 6x2 − 4x − 6
- d/dx(2x3) = 6x2
- d/dx(−2x2) = −4x
- d/dx(−6x) = −6
8.Differentiate y = −5x2 − 3x + 6
Answer: dy/dx = −10x − 3
- d/dx(−5x2) = −10x
- d/dx(−3x) = −3
- The derivative of the constant 6 is 0
9.Differentiate y = 5x5 + 5x4 − 4
Answer: dy/dx = 25x4 + 20x3
- d/dx(5x5) = 25x4
- d/dx(5x4) = 20x3
- The derivative of the constant −4 is 0
10.Differentiate y = 2x5 + 4x2 − 2
Answer: dy/dx = 10x4 + 8x
- d/dx(2x5) = 10x4
- d/dx(4x2) = 8x
- The derivative of the constant −2 is 0
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