Year 13 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Answer sheet with worked solutions for the Year 13 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · CalculusYear 13 Differentiation (Power Rule) Worksheet — Level 1 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 6x3 + 6
Answer: dy/dx = 18x2
- d/dx(6x3) = 18x2
- The derivative of the constant 6 is 0
2.Differentiate y = −x3 + 3
Answer: dy/dx = −3x2
- d/dx(−x3) = −3x2
- The derivative of the constant 3 is 0
3.Differentiate y = −2x3 + 4x
Answer: dy/dx = −6x2 + 4
- d/dx(−2x3) = −6x2
- d/dx(4x) = 4
4.Differentiate y = −5x2 − 6x
Answer: dy/dx = −10x − 6
- d/dx(−5x2) = −10x
- d/dx(−6x) = −6
5.Differentiate y = 5x2 + 7x
Answer: dy/dx = 10x + 7
- d/dx(5x2) = 10x
- d/dx(7x) = 7
6.Differentiate y = −x2 − 7x
Answer: dy/dx = −2x − 7
- d/dx(−x2) = −2x
- d/dx(−7x) = −7
7.Differentiate y = 3x3 + 6x
Answer: dy/dx = 9x2 + 6
- d/dx(3x3) = 9x2
- d/dx(6x) = 6
8.Differentiate y = −2x2 + 4x
Answer: dy/dx = −4x + 4
- d/dx(−2x2) = −4x
- d/dx(4x) = 4
9.Differentiate y = 6x3 + 7x2
Answer: dy/dx = 18x2 + 14x
- d/dx(6x3) = 18x2
- d/dx(7x2) = 14x
10.Differentiate y = x − 1
Answer: dy/dx = 1
- d/dx(x) = 1
- The derivative of the constant −1 is 0
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