Year 12 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 7x5 − 5x2 + 3, find f′(1).
Answer: f′(1) = 25
- d/dx(7x5) = 35x4
- d/dx(−5x2) = −10x
- The derivative of the constant 3 is 0
- f′(x) = 35x4 − 10x
- Substitute x = 1: 25
2.If f(x) = −4x6 − 6x3 − 2, find f′(1).
Answer: f′(1) = −42
- d/dx(−4x6) = −24x5
- d/dx(−6x3) = −18x2
- The derivative of the constant −2 is 0
- f′(x) = −24x5 − 18x2
- Substitute x = 1: −42
3.If f(x) = 7x6 + 8x5 + x4, find f′(−2).
Answer: f′(−2) = −736
- d/dx(7x6) = 42x5
- d/dx(8x5) = 40x4
- d/dx(x4) = 4x3
- f′(x) = 42x5 + 40x4 + 4x3
- Substitute x = −2: −736
4.Differentiate y = 4x4 + 8x2 + 5
Answer: dy/dx = 16x3 + 16x
- d/dx(4x4) = 16x3
- d/dx(8x2) = 16x
- The derivative of the constant 5 is 0
5.If f(x) = 9x5 + 5x + 4, find f′(1).
Answer: f′(1) = 50
- d/dx(9x5) = 45x4
- d/dx(5x) = 5
- The derivative of the constant 4 is 0
- f′(x) = 45x4 + 5
- Substitute x = 1: 50
6.Differentiate y = −6x6 + x5 + 2x3
Answer: dy/dx = −36x5 + 5x4 + 6x2
- d/dx(−6x6) = −36x5
- d/dx(x5) = 5x4
- d/dx(2x3) = 6x2
7.Differentiate y = 2x6 + 4x5 + x3
Answer: dy/dx = 12x5 + 20x4 + 3x2
- d/dx(2x6) = 12x5
- d/dx(4x5) = 20x4
- d/dx(x3) = 3x2
8.If f(x) = 4x4 + 3x3 + 2, find f′(−2).
Answer: f′(−2) = −92
- d/dx(4x4) = 16x3
- d/dx(3x3) = 9x2
- The derivative of the constant 2 is 0
- f′(x) = 16x3 + 9x2
- Substitute x = −2: −92
9.Differentiate y = −x5 + 7x3 − 2x2
Answer: dy/dx = −5x4 + 21x2 − 4x
- d/dx(−x5) = −5x4
- d/dx(7x3) = 21x2
- d/dx(−2x2) = −4x
10.Differentiate y = x6 + 9x2 − 6x
Answer: dy/dx = 6x5 + 18x − 6
- d/dx(x6) = 6x5
- d/dx(9x2) = 18x
- d/dx(−6x) = −6
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