Year 13 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 3 — Answers
Answer sheet with worked solutions for the Year 13 calculus worksheet.
Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · CalculusYear 13 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −7x4 + 6x3 − 6x2
Answer: dy/dx = −28x3 + 18x2 − 12x
- d/dx(−7x4) = −28x3
- d/dx(6x3) = 18x2
- d/dx(−6x2) = −12x
2.Differentiate y = 7x5 + 9x3 + 4x2
Answer: dy/dx = 35x4 + 27x2 + 8x
- d/dx(7x5) = 35x4
- d/dx(9x3) = 27x2
- d/dx(4x2) = 8x
3.Differentiate y = −5x5 + 5x2 − 2x
Answer: dy/dx = −25x4 + 10x − 2
- d/dx(−5x5) = −25x4
- d/dx(5x2) = 10x
- d/dx(−2x) = −2
4.Differentiate y = 3x4 − 7x2 − 7
Answer: dy/dx = 12x3 − 14x
- d/dx(3x4) = 12x3
- d/dx(−7x2) = −14x
- The derivative of the constant −7 is 0
5.Differentiate y = −x5 − 4x4 + 4x
Answer: dy/dx = −5x4 − 16x3 + 4
- d/dx(−x5) = −5x4
- d/dx(−4x4) = −16x3
- d/dx(4x) = 4
6.Differentiate y = 7x4 − x − 7
Answer: dy/dx = 28x3 − 1
- d/dx(7x4) = 28x3
- d/dx(−x) = −1
- The derivative of the constant −7 is 0
7.Differentiate y = 2x5 − 6x4 + 3x3
Answer: dy/dx = 10x4 − 24x3 + 9x2
- d/dx(2x5) = 10x4
- d/dx(−6x4) = −24x3
- d/dx(3x3) = 9x2
8.Differentiate y = 6x5 − x3 − 5x
Answer: dy/dx = 30x4 − 3x2 − 5
- d/dx(6x5) = 30x4
- d/dx(−x3) = −3x2
- d/dx(−5x) = −5
9.Differentiate y = −x5 − 7x3 + 6
Answer: dy/dx = −5x4 − 21x2
- d/dx(−x5) = −5x4
- d/dx(−7x3) = −21x2
- The derivative of the constant 6 is 0
10.Differentiate y = −4x5 − x4 + 2x2
Answer: dy/dx = −20x4 − 4x3 + 4x
- d/dx(−4x5) = −20x4
- d/dx(−x4) = −4x3
- d/dx(2x2) = 4x
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