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 = −4x4 − 4x3 + 6
Answer: dy/dx = −16x3 − 12x2
- d/dx(−4x4) = −16x3
- d/dx(−4x3) = −12x2
- The derivative of the constant 6 is 0
2.Differentiate y = −5x4 − 7x3 + 2x2
Answer: dy/dx = −20x3 − 21x2 + 4x
- d/dx(−5x4) = −20x3
- d/dx(−7x3) = −21x2
- d/dx(2x2) = 4x
3.If f(x) = −5x6 + 3x5 − 3x, find f′(−1).
Answer: f′(−1) = 42
- d/dx(−5x6) = −30x5
- d/dx(3x5) = 15x4
- d/dx(−3x) = −3
- f′(x) = −30x5 + 15x4 − 3
- Substitute x = −1: 42
4.Differentiate y = −5x6 + 7x3 − 2x2
Answer: dy/dx = −30x5 + 21x2 − 4x
- d/dx(−5x6) = −30x5
- d/dx(7x3) = 21x2
- d/dx(−2x2) = −4x
5.Differentiate y = −5x6 + 3x5 − x3
Answer: dy/dx = −30x5 + 15x4 − 3x2
- d/dx(−5x6) = −30x5
- d/dx(3x5) = 15x4
- d/dx(−x3) = −3x2
6.If f(x) = x5 − 5x2 + 4x, find f′(1).
Answer: f′(1) = −1
- d/dx(x5) = 5x4
- d/dx(−5x2) = −10x
- d/dx(4x) = 4
- f′(x) = 5x4 − 10x + 4
- Substitute x = 1: −1
7.If f(x) = 5x6 + 5x3 + 2, find f′(1).
Answer: f′(1) = 45
- d/dx(5x6) = 30x5
- d/dx(5x3) = 15x2
- The derivative of the constant 2 is 0
- f′(x) = 30x5 + 15x2
- Substitute x = 1: 45
8.Differentiate y = −7x6 − 3x3 − 3
Answer: dy/dx = −42x5 − 9x2
- d/dx(−7x6) = −42x5
- d/dx(−3x3) = −9x2
- The derivative of the constant −3 is 0
9.Differentiate y = −6x6 + 3x5 − 4x4
Answer: dy/dx = −36x5 + 15x4 − 16x3
- d/dx(−6x6) = −36x5
- d/dx(3x5) = 15x4
- d/dx(−4x4) = −16x3
10.If f(x) = 8x6 + 2x3 − 6x, find f′(1).
Answer: f′(1) = 48
- d/dx(8x6) = 48x5
- d/dx(2x3) = 6x2
- d/dx(−6x) = −6
- f′(x) = 48x5 + 6x2 − 6
- Substitute x = 1: 48
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