Year 11 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 9x3 − 7x + 6, find f′(2).
Answer: f′(2) = 101
- d/dx(9x3) = 27x2
- d/dx(−7x) = −7
- The derivative of the constant 6 is 0
- f′(x) = 27x2 − 7
- Substitute x = 2: 101
2.Differentiate y = 6x4 − 7x3 − 4x2
Answer: dy/dx = 24x3 − 21x2 − 8x
- d/dx(6x4) = 24x3
- d/dx(−7x3) = −21x2
- d/dx(−4x2) = −8x
3.If f(x) = 7x4 + 5x3 + 4x2, find f′(−1).
Answer: f′(−1) = −21
- d/dx(7x4) = 28x3
- d/dx(5x3) = 15x2
- d/dx(4x2) = 8x
- f′(x) = 28x3 + 15x2 + 8x
- Substitute x = −1: −21
4.If f(x) = −2x4 + 4x3 + 8, find f′(2).
Answer: f′(2) = −16
- d/dx(−2x4) = −8x3
- d/dx(4x3) = 12x2
- The derivative of the constant 8 is 0
- f′(x) = −8x3 + 12x2
- Substitute x = 2: −16
5.Differentiate y = 2x3 + 6x2 + 2x
Answer: dy/dx = 6x2 + 12x + 2
- d/dx(2x3) = 6x2
- d/dx(6x2) = 12x
- d/dx(2x) = 2
6.Differentiate y = 4x5 + 6x4 + 7
Answer: dy/dx = 20x4 + 24x3
- d/dx(4x5) = 20x4
- d/dx(6x4) = 24x3
- The derivative of the constant 7 is 0
7.Differentiate y = 9x5 + 6x4 + 3
Answer: dy/dx = 45x4 + 24x3
- d/dx(9x5) = 45x4
- d/dx(6x4) = 24x3
- The derivative of the constant 3 is 0
8.Differentiate y = −5x4 + 8x2 + 4x
Answer: dy/dx = −20x3 + 16x + 4
- d/dx(−5x4) = −20x3
- d/dx(8x2) = 16x
- d/dx(4x) = 4
9.If f(x) = −4x6 + 7x5 − 7x2, find f′(−2).
Answer: f′(−2) = 1356
- d/dx(−4x6) = −24x5
- d/dx(7x5) = 35x4
- d/dx(−7x2) = −14x
- f′(x) = −24x5 + 35x4 − 14x
- Substitute x = −2: 1356
10.If f(x) = −6x6 + 8x + 7, find f′(−2).
Answer: f′(−2) = 1160
- d/dx(−6x6) = −36x5
- d/dx(8x) = 8
- The derivative of the constant 7 is 0
- f′(x) = −36x5 + 8
- Substitute x = −2: 1160
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