Year 13 Differentiation (Power Rule) Worksheet — Level 3 — Answers
Answer sheet with worked solutions for the Year 13 calculus worksheet.
Year 13 · Mathematics · Calculus
Year 13 Differentiation (Power Rule) Worksheet — Level 3 — Answers
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Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 9x6 − 2x2 − 7
Answer: dy/dx = 54x5 − 4x
- d/dx(9x6) = 54x5
- d/dx(−2x2) = −4x
- The derivative of the constant −7 is 0
2.Differentiate y = 5x5 − 4x4 − 6x2
Answer: dy/dx = 25x4 − 16x3 − 12x
- d/dx(5x5) = 25x4
- d/dx(−4x4) = −16x3
- d/dx(−6x2) = −12x
3.If f(x) = x5 + 7x3 − 4x2, find f′(2).
Answer: f′(2) = 148
- d/dx(x5) = 5x4
- d/dx(7x3) = 21x2
- d/dx(−4x2) = −8x
- f′(x) = 5x4 + 21x2 − 8x
- Substitute x = 2: 148
4.Differentiate y = 2x6 + 7x3 + 2
Answer: dy/dx = 12x5 + 21x2
- d/dx(2x6) = 12x5
- d/dx(7x3) = 21x2
- The derivative of the constant 2 is 0
5.Differentiate y = 2x4 − 5x3 − 4x2
Answer: dy/dx = 8x3 − 15x2 − 8x
- d/dx(2x4) = 8x3
- d/dx(−5x3) = −15x2
- d/dx(−4x2) = −8x
6.Differentiate y = −6x6 + 3x4 + 9
Answer: dy/dx = −36x5 + 12x3
- d/dx(−6x6) = −36x5
- d/dx(3x4) = 12x3
- The derivative of the constant 9 is 0
7.If f(x) = 7x6 − 4x4 + 7x2, find f′(2).
Answer: f′(2) = 1244
- d/dx(7x6) = 42x5
- d/dx(−4x4) = −16x3
- d/dx(7x2) = 14x
- f′(x) = 42x5 − 16x3 + 14x
- Substitute x = 2: 1244
8.If f(x) = 2x3 − 5x2 − 6x, find f′(−1).
Answer: f′(−1) = 10
- d/dx(2x3) = 6x2
- d/dx(−5x2) = −10x
- d/dx(−6x) = −6
- f′(x) = 6x2 − 10x − 6
- Substitute x = −1: 10
9.Differentiate y = −4x5 + 3x2 − x
Answer: dy/dx = −20x4 + 6x − 1
- d/dx(−4x5) = −20x4
- d/dx(3x2) = 6x
- d/dx(−x) = −1
10.Differentiate y = 7x5 + 9x3 + 4
Answer: dy/dx = 35x4 + 27x2
- d/dx(7x5) = 35x4
- d/dx(9x3) = 27x2
- The derivative of the constant 4 is 0
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