Year 12 Differentiation (Power Rule) Worksheet — Level 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −3x4 − 5x3 + 9
Answer: dy/dx = −12x3 − 15x2
- d/dx(−3x4) = −12x3
- d/dx(−5x3) = −15x2
- The derivative of the constant 9 is 0
2.Differentiate y = −3x5 − x4 − 4x2
Answer: dy/dx = −15x4 − 4x3 − 8x
- d/dx(−3x5) = −15x4
- d/dx(−x4) = −4x3
- d/dx(−4x2) = −8x
3.Differentiate y = −4x5 + 9x4 + 5
Answer: dy/dx = −20x4 + 36x3
- d/dx(−4x5) = −20x4
- d/dx(9x4) = 36x3
- The derivative of the constant 5 is 0
4.Differentiate y = −7x4 + 8x2 + 3x
Answer: dy/dx = −28x3 + 16x + 3
- d/dx(−7x4) = −28x3
- d/dx(8x2) = 16x
- d/dx(3x) = 3
5.Differentiate y = 8x5 + 7x + 9
Answer: dy/dx = 40x4 + 7
- d/dx(8x5) = 40x4
- d/dx(7x) = 7
- The derivative of the constant 9 is 0
6.Differentiate y = −4x4 − 6x − 5
Answer: dy/dx = −16x3 − 6
- d/dx(−4x4) = −16x3
- d/dx(−6x) = −6
- The derivative of the constant −5 is 0
7.Differentiate y = −4x5 + 9x − 2
Answer: dy/dx = −20x4 + 9
- d/dx(−4x5) = −20x4
- d/dx(9x) = 9
- The derivative of the constant −2 is 0
8.Differentiate y = 8x2 − x + 6
Answer: dy/dx = 16x − 1
- d/dx(8x2) = 16x
- d/dx(−x) = −1
- The derivative of the constant 6 is 0
9.Differentiate y = −7x3 − 5x2 + 4x
Answer: dy/dx = −21x2 − 10x + 4
- d/dx(−7x3) = −21x2
- d/dx(−5x2) = −10x
- d/dx(4x) = 4
10.Differentiate y = 3x4 + 3x2 − 7x
Answer: dy/dx = 12x3 + 6x − 7
- d/dx(3x4) = 12x3
- d/dx(3x2) = 6x
- d/dx(−7x) = −7
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