Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the Year 12 calculus worksheet.
Year 12 · Mathematics · Calculus
Year 12 Differentiation (Power Rule) Worksheet — Level 2 — Answers
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Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −4x5 − 2x3 + 8
Answer: dy/dx = −20x4 − 6x2
- d/dx(−4x5) = −20x4
- d/dx(−2x3) = −6x2
- The derivative of the constant 8 is 0
2.Differentiate y = −7x5 + 6x3 − 7x2
Answer: dy/dx = −35x4 + 18x2 − 14x
- d/dx(−7x5) = −35x4
- d/dx(6x3) = 18x2
- d/dx(−7x2) = −14x
3.Differentiate y = 5x5 + 3x4 − 4
Answer: dy/dx = 25x4 + 12x3
- d/dx(5x5) = 25x4
- d/dx(3x4) = 12x3
- The derivative of the constant −4 is 0
4.Differentiate y = −x5 + 9x4 − 4x2
Answer: dy/dx = −5x4 + 36x3 − 8x
- d/dx(−x5) = −5x4
- d/dx(9x4) = 36x3
- d/dx(−4x2) = −8x
5.Differentiate y = 4x4 + 5x2 + 9x
Answer: dy/dx = 16x3 + 10x + 9
- d/dx(4x4) = 16x3
- d/dx(5x2) = 10x
- d/dx(9x) = 9
6.Differentiate y = −x4 + 7x2 − 4
Answer: dy/dx = −4x3 + 14x
- d/dx(−x4) = −4x3
- d/dx(7x2) = 14x
- The derivative of the constant −4 is 0
7.Differentiate y = −3x5 − 5x4 + 9x3
Answer: dy/dx = −15x4 − 20x3 + 27x2
- d/dx(−3x5) = −15x4
- d/dx(−5x4) = −20x3
- d/dx(9x3) = 27x2
8.Differentiate y = 9x5 − 4x4 − 5x2
Answer: dy/dx = 45x4 − 16x3 − 10x
- d/dx(9x5) = 45x4
- d/dx(−4x4) = −16x3
- d/dx(−5x2) = −10x
9.Differentiate y = 3x5 + 5x2 + x
Answer: dy/dx = 15x4 + 10x + 1
- d/dx(3x5) = 15x4
- d/dx(5x2) = 10x
- d/dx(x) = 1
10.Differentiate y = x4 − x3 − 3x2
Answer: dy/dx = 4x3 − 3x2 − 6x
- d/dx(x4) = 4x3
- d/dx(−x3) = −3x2
- d/dx(−3x2) = −6x
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