Year 13 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 2 — 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 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −x − 4
Answer: dy/dx = −1
- d/dx(−x) = −1
- The derivative of the constant −4 is 0
2.Differentiate y = 8x − 5
Answer: dy/dx = 8
- d/dx(8x) = 8
- The derivative of the constant −5 is 0
3.Differentiate y = −3x2 − 4x
Answer: dy/dx = −6x − 4
- d/dx(−3x2) = −6x
- d/dx(−4x) = −4
4.Differentiate y = 3x2 + 8x
Answer: dy/dx = 6x + 8
- d/dx(3x2) = 6x
- d/dx(8x) = 8
5.Differentiate y = −7x3 + 9x2
Answer: dy/dx = −21x2 + 18x
- d/dx(−7x3) = −21x2
- d/dx(9x2) = 18x
6.Differentiate y = 4x2 + x
Answer: dy/dx = 8x + 1
- d/dx(4x2) = 8x
- d/dx(x) = 1
7.Differentiate y = 6x2 + 7x
Answer: dy/dx = 12x + 7
- d/dx(6x2) = 12x
- d/dx(7x) = 7
8.Differentiate y = −7x3 + 9x
Answer: dy/dx = −21x2 + 9
- d/dx(−7x3) = −21x2
- d/dx(9x) = 9
9.Differentiate y = −5x3 − 2x
Answer: dy/dx = −15x2 − 2
- d/dx(−5x3) = −15x2
- d/dx(−2x) = −2
10.Differentiate y = 7x3 + 8x2
Answer: dy/dx = 21x2 + 16x
- d/dx(7x3) = 21x2
- d/dx(8x2) = 16x
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