Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 3 — 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 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 9x3 + x − 3
Answer: dy/dx = 27x2 + 1
- d/dx(9x3) = 27x2
- d/dx(x) = 1
- The derivative of the constant −3 is 0
2.Differentiate y = 2x5 + 8x3 − 5
Answer: dy/dx = 10x4 + 24x2
- d/dx(2x5) = 10x4
- d/dx(8x3) = 24x2
- The derivative of the constant −5 is 0
3.Differentiate y = 8x5 − 6x4 − 6x2
Answer: dy/dx = 40x4 − 24x3 − 12x
- d/dx(8x5) = 40x4
- d/dx(−6x4) = −24x3
- d/dx(−6x2) = −12x
4.Differentiate y = −x5 + 6x2 + x
Answer: dy/dx = −5x4 + 12x + 1
- d/dx(−x5) = −5x4
- d/dx(6x2) = 12x
- d/dx(x) = 1
5.Differentiate y = 6x3 + 9x2 + 6
Answer: dy/dx = 18x2 + 18x
- d/dx(6x3) = 18x2
- d/dx(9x2) = 18x
- The derivative of the constant 6 is 0
6.Differentiate y = −4x5 + 5x3 − 5x
Answer: dy/dx = −20x4 + 15x2 − 5
- d/dx(−4x5) = −20x4
- d/dx(5x3) = 15x2
- d/dx(−5x) = −5
7.Differentiate y = 3x4 + 5x2 − 1
Answer: dy/dx = 12x3 + 10x
- d/dx(3x4) = 12x3
- d/dx(5x2) = 10x
- The derivative of the constant −1 is 0
8.Differentiate y = −3x2 − 4x − 2
Answer: dy/dx = −6x − 4
- d/dx(−3x2) = −6x
- d/dx(−4x) = −4
- The derivative of the constant −2 is 0
9.Differentiate y = −2x5 + 3x4 + 8x
Answer: dy/dx = −10x4 + 12x3 + 8
- d/dx(−2x5) = −10x4
- d/dx(3x4) = 12x3
- d/dx(8x) = 8
10.Differentiate y = 5x4 + 7x3 + 1
Answer: dy/dx = 20x3 + 21x2
- d/dx(5x4) = 20x3
- d/dx(7x3) = 21x2
- The derivative of the constant 1 is 0
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