Year 11 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the Year 11 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · CalculusYear 11 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = x3 − 6x2 + 6x
Answer: dy/dx = 3x2 − 12x + 6
- d/dx(x3) = 3x2
- d/dx(−6x2) = −12x
- d/dx(6x) = 6
2.Differentiate y = 7x4 + 6x3 − 7
Answer: dy/dx = 28x3 + 18x2
- d/dx(7x4) = 28x3
- d/dx(6x3) = 18x2
- The derivative of the constant −7 is 0
3.If f(x) = 9x6 + 8x + 2, find f′(2).
Answer: f′(2) = 1736
- d/dx(9x6) = 54x5
- d/dx(8x) = 8
- The derivative of the constant 2 is 0
- f′(x) = 54x5 + 8
- Substitute x = 2: 1736
4.Differentiate y = 5x6 + 7x2 − 1
Answer: dy/dx = 30x5 + 14x
- d/dx(5x6) = 30x5
- d/dx(7x2) = 14x
- The derivative of the constant −1 is 0
5.If f(x) = 4x4 − 5x3 + 2, find f′(−1).
Answer: f′(−1) = −31
- d/dx(4x4) = 16x3
- d/dx(−5x3) = −15x2
- The derivative of the constant 2 is 0
- f′(x) = 16x3 − 15x2
- Substitute x = −1: −31
6.Differentiate y = −5x5 + 7x4 − 2x2
Answer: dy/dx = −25x4 + 28x3 − 4x
- d/dx(−5x5) = −25x4
- d/dx(7x4) = 28x3
- d/dx(−2x2) = −4x
7.Differentiate y = 9x6 − 6x5 − 4
Answer: dy/dx = 54x5 − 30x4
- d/dx(9x6) = 54x5
- d/dx(−6x5) = −30x4
- The derivative of the constant −4 is 0
8.If f(x) = 7x6 + 9x5 + 2, find f′(−2).
Answer: f′(−2) = −624
- d/dx(7x6) = 42x5
- d/dx(9x5) = 45x4
- The derivative of the constant 2 is 0
- f′(x) = 42x5 + 45x4
- Substitute x = −2: −624
9.Differentiate y = 2x6 − 6x2 − 2
Answer: dy/dx = 12x5 − 12x
- d/dx(2x6) = 12x5
- d/dx(−6x2) = −12x
- The derivative of the constant −2 is 0
10.Differentiate y = −5x5 + 2x4 + 6x3
Answer: dy/dx = −25x4 + 8x3 + 18x2
- d/dx(−5x5) = −25x4
- d/dx(2x4) = 8x3
- d/dx(6x3) = 18x2
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