Year 12 Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 2 — 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 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 5x6 + 7x5 − 1
Answer: dy/dx = 30x5 + 35x4
- d/dx(5x6) = 30x5
- d/dx(7x5) = 35x4
- The derivative of the constant −1 is 0
2.If f(x) = 7x6 − x5 − 6x3, find f′(2).
Answer: f′(2) = 1192
- d/dx(7x6) = 42x5
- d/dx(−x5) = −5x4
- d/dx(−6x3) = −18x2
- f′(x) = 42x5 − 5x4 − 18x2
- Substitute x = 2: 1192
3.If f(x) = −5x4 + 7x2 − 2x, find f′(2).
Answer: f′(2) = −134
- d/dx(−5x4) = −20x3
- d/dx(7x2) = 14x
- d/dx(−2x) = −2
- f′(x) = −20x3 + 14x − 2
- Substitute x = 2: −134
4.If f(x) = −x5 − 6x2 + x, find f′(1).
Answer: f′(1) = −16
- d/dx(−x5) = −5x4
- d/dx(−6x2) = −12x
- d/dx(x) = 1
- f′(x) = −5x4 − 12x + 1
- Substitute x = 1: −16
5.Differentiate y = 7x5 − 5x2 + 2x
Answer: dy/dx = 35x4 − 10x + 2
- d/dx(7x5) = 35x4
- d/dx(−5x2) = −10x
- d/dx(2x) = 2
6.If f(x) = −x5 + 2x − 4, find f′(2).
Answer: f′(2) = −78
- d/dx(−x5) = −5x4
- d/dx(2x) = 2
- The derivative of the constant −4 is 0
- f′(x) = −5x4 + 2
- Substitute x = 2: −78
7.Differentiate y = −4x6 + x5 − 2
Answer: dy/dx = −24x5 + 5x4
- d/dx(−4x6) = −24x5
- d/dx(x5) = 5x4
- The derivative of the constant −2 is 0
8.If f(x) = 2x3 + 8x2 + 1, find f′(−2).
Answer: f′(−2) = −8
- d/dx(2x3) = 6x2
- d/dx(8x2) = 16x
- The derivative of the constant 1 is 0
- f′(x) = 6x2 + 16x
- Substitute x = −2: −8
9.If f(x) = 8x6 + 7x4 − 4x3, find f′(1).
Answer: f′(1) = 64
- d/dx(8x6) = 48x5
- d/dx(7x4) = 28x3
- d/dx(−4x3) = −12x2
- f′(x) = 48x5 + 28x3 − 12x2
- Substitute x = 1: 64
10.If f(x) = 8x5 + 7x4 − 1, find f′(1).
Answer: f′(1) = 68
- d/dx(8x5) = 40x4
- d/dx(7x4) = 28x3
- The derivative of the constant −1 is 0
- f′(x) = 40x4 + 28x3
- Substitute x = 1: 68
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