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