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