Year 12 Differentiation (Power Rule) Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 4x6 + 6x4 + 3x3
Answer: dy/dx = 24x5 + 24x3 + 9x2
- d/dx(4x6) = 24x5
- d/dx(6x4) = 24x3
- d/dx(3x3) = 9x2
2.Differentiate y = 7x2 + 6x + 9
Answer: dy/dx = 14x + 6
- d/dx(7x2) = 14x
- d/dx(6x) = 6
- The derivative of the constant 9 is 0
3.If f(x) = −3x6 − 5x3 − 2x, find f′(1).
Answer: f′(1) = −35
- d/dx(−3x6) = −18x5
- d/dx(−5x3) = −15x2
- d/dx(−2x) = −2
- f′(x) = −18x5 − 15x2 − 2
- Substitute x = 1: −35
4.If f(x) = −4x6 − 2x4 + 5x3, find f′(−2).
Answer: f′(−2) = 892
- d/dx(−4x6) = −24x5
- d/dx(−2x4) = −8x3
- d/dx(5x3) = 15x2
- f′(x) = −24x5 − 8x3 + 15x2
- Substitute x = −2: 892
5.If f(x) = −6x6 − x3 + 4x, find f′(2).
Answer: f′(2) = −1160
- d/dx(−6x6) = −36x5
- d/dx(−x3) = −3x2
- d/dx(4x) = 4
- f′(x) = −36x5 − 3x2 + 4
- Substitute x = 2: −1160
6.If f(x) = 3x6 − 6x4 − 3x, find f′(−1).
Answer: f′(−1) = 3
- d/dx(3x6) = 18x5
- d/dx(−6x4) = −24x3
- d/dx(−3x) = −3
- f′(x) = 18x5 − 24x3 − 3
- Substitute x = −1: 3
7.Differentiate y = x6 − 2x4 + 9
Answer: dy/dx = 6x5 − 8x3
- d/dx(x6) = 6x5
- d/dx(−2x4) = −8x3
- The derivative of the constant 9 is 0
8.Differentiate y = −3x6 − 6x + 5
Answer: dy/dx = −18x5 − 6
- d/dx(−3x6) = −18x5
- d/dx(−6x) = −6
- The derivative of the constant 5 is 0
9.Differentiate y = −3x5 + 4x2 − 4
Answer: dy/dx = −15x4 + 8x
- d/dx(−3x5) = −15x4
- d/dx(4x2) = 8x
- The derivative of the constant −4 is 0
10.Differentiate y = −7x6 + x − 1
Answer: dy/dx = −42x5 + 1
- d/dx(−7x6) = −42x5
- d/dx(x) = 1
- The derivative of the constant −1 is 0
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