Year 13 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −2x2 − 3
Answer: dy/dx = −4x
- d/dx(−2x2) = −4x
- The derivative of the constant −3 is 0
2.Differentiate y = 4x3 + 2x
Answer: dy/dx = 12x2 + 2
- d/dx(4x3) = 12x2
- d/dx(2x) = 2
3.Differentiate y = −2x + 3
Answer: dy/dx = −2
- d/dx(−2x) = −2
- The derivative of the constant 3 is 0
4.Differentiate y = −3x3 + 2x
Answer: dy/dx = −9x2 + 2
- d/dx(−3x3) = −9x2
- d/dx(2x) = 2
5.Differentiate y = 5x3 − 7x
Answer: dy/dx = 15x2 − 7
- d/dx(5x3) = 15x2
- d/dx(−7x) = −7
6.Differentiate y = 9x3 + 7
Answer: dy/dx = 27x2
- d/dx(9x3) = 27x2
- The derivative of the constant 7 is 0
7.Differentiate y = 6x3 + x
Answer: dy/dx = 18x2 + 1
- d/dx(6x3) = 18x2
- d/dx(x) = 1
8.Differentiate y = 7x + 4
Answer: dy/dx = 7
- d/dx(7x) = 7
- The derivative of the constant 4 is 0
9.Differentiate y = 6x − 2
Answer: dy/dx = 6
- d/dx(6x) = 6
- The derivative of the constant −2 is 0
10.Differentiate y = 2x3 − 5
Answer: dy/dx = 6x2
- d/dx(2x3) = 6x2
- The derivative of the constant −5 is 0
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