Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 3x4 + 2x3 + 4
Answer: dy/dx = 12x3 + 6x2
- d/dx(3x4) = 12x3
- d/dx(2x3) = 6x2
- The derivative of the constant 4 is 0
2.Differentiate y = −5x3 − 2x − 2
Answer: dy/dx = −15x2 − 2
- d/dx(−5x3) = −15x2
- d/dx(−2x) = −2
- The derivative of the constant −2 is 0
3.Differentiate y = −5x5 − 2x4 + 6x
Answer: dy/dx = −25x4 − 8x3 + 6
- d/dx(−5x5) = −25x4
- d/dx(−2x4) = −8x3
- d/dx(6x) = 6
4.Differentiate y = −2x5 + 2x3 + 2x2
Answer: dy/dx = −10x4 + 6x2 + 4x
- d/dx(−2x5) = −10x4
- d/dx(2x3) = 6x2
- d/dx(2x2) = 4x
5.Differentiate y = −5x5 + 8x4 + 6
Answer: dy/dx = −25x4 + 32x3
- d/dx(−5x5) = −25x4
- d/dx(8x4) = 32x3
- The derivative of the constant 6 is 0
6.Differentiate y = 5x5 + 8x2 − 4x
Answer: dy/dx = 25x4 + 16x − 4
- d/dx(5x5) = 25x4
- d/dx(8x2) = 16x
- d/dx(−4x) = −4
7.Differentiate y = 3x5 + 2x2 + 5
Answer: dy/dx = 15x4 + 4x
- d/dx(3x5) = 15x4
- d/dx(2x2) = 4x
- The derivative of the constant 5 is 0
8.Differentiate y = −2x4 − 4x3 + 5x
Answer: dy/dx = −8x3 − 12x2 + 5
- d/dx(−2x4) = −8x3
- d/dx(−4x3) = −12x2
- d/dx(5x) = 5
9.Differentiate y = 2x5 + 4x4 + 8x
Answer: dy/dx = 10x4 + 16x3 + 8
- d/dx(2x5) = 10x4
- d/dx(4x4) = 16x3
- d/dx(8x) = 8
10.Differentiate y = −2x3 + 9x2 − 2x
Answer: dy/dx = −6x2 + 18x − 2
- d/dx(−2x3) = −6x2
- d/dx(9x2) = 18x
- d/dx(−2x) = −2
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