Year 13 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 3 — 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 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 9x2 + 7x
Answer: dy/dx = 18x + 7
- d/dx(9x2) = 18x
- d/dx(7x) = 7
2.Differentiate y = −5x − 5
Answer: dy/dx = −5
- d/dx(−5x) = −5
- The derivative of the constant −5 is 0
3.Differentiate y = 3x3 − 7x
Answer: dy/dx = 9x2 − 7
- d/dx(3x3) = 9x2
- d/dx(−7x) = −7
4.Differentiate y = −2x − 1
Answer: dy/dx = −2
- d/dx(−2x) = −2
- The derivative of the constant −1 is 0
5.Differentiate y = 3x + 8
Answer: dy/dx = 3
- d/dx(3x) = 3
- The derivative of the constant 8 is 0
6.Differentiate y = −x − 5
Answer: dy/dx = −1
- d/dx(−x) = −1
- The derivative of the constant −5 is 0
7.Differentiate y = −6x + 8
Answer: dy/dx = −6
- d/dx(−6x) = −6
- The derivative of the constant 8 is 0
8.Differentiate y = 8x2 − 2
Answer: dy/dx = 16x
- d/dx(8x2) = 16x
- The derivative of the constant −2 is 0
9.Differentiate y = 6x3 + 6x2
Answer: dy/dx = 18x2 + 12x
- d/dx(6x3) = 18x2
- d/dx(6x2) = 12x
10.Differentiate y = −4x3 + 5x2
Answer: dy/dx = −12x2 + 10x
- d/dx(−4x3) = −12x2
- d/dx(5x2) = 10x
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