Year 12 Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 3 — 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 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 4x + 5
Answer: dy/dx = 4
- d/dx(4x) = 4
- The derivative of the constant 5 is 0
2.Differentiate y = 5x + 2
Answer: dy/dx = 5
- d/dx(5x) = 5
- The derivative of the constant 2 is 0
3.Differentiate y = −4x2 − 2
Answer: dy/dx = −8x
- d/dx(−4x2) = −8x
- The derivative of the constant −2 is 0
4.Differentiate y = −7x3 + 8x
Answer: dy/dx = −21x2 + 8
- d/dx(−7x3) = −21x2
- d/dx(8x) = 8
5.Differentiate y = −4x3 + x2
Answer: dy/dx = −12x2 + 2x
- d/dx(−4x3) = −12x2
- d/dx(x2) = 2x
6.Differentiate y = 8x3 − 5
Answer: dy/dx = 24x2
- d/dx(8x3) = 24x2
- The derivative of the constant −5 is 0
7.Differentiate y = 9x + 4
Answer: dy/dx = 9
- d/dx(9x) = 9
- The derivative of the constant 4 is 0
8.Differentiate y = 7x − 1
Answer: dy/dx = 7
- d/dx(7x) = 7
- The derivative of the constant −1 is 0
9.Differentiate y = −4x3 + 4x2
Answer: dy/dx = −12x2 + 8x
- d/dx(−4x3) = −12x2
- d/dx(4x2) = 8x
10.Differentiate y = −x + 7
Answer: dy/dx = −1
- d/dx(−x) = −1
- The derivative of the constant 7 is 0
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