Year 13 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −7x4 + 8x2 − 4
Answer: dy/dx = −28x3 + 16x
- d/dx(−7x4) = −28x3
- d/dx(8x2) = 16x
- The derivative of the constant −4 is 0
2.Differentiate y = x4 + 7x3 − x
Answer: dy/dx = 4x3 + 21x2 − 1
- d/dx(x4) = 4x3
- d/dx(7x3) = 21x2
- d/dx(−x) = −1
3.Differentiate y = 2x5 − 7x + 6
Answer: dy/dx = 10x4 − 7
- d/dx(2x5) = 10x4
- d/dx(−7x) = −7
- The derivative of the constant 6 is 0
4.Differentiate y = −6x5 − 3x3 + x
Answer: dy/dx = −30x4 − 9x2 + 1
- d/dx(−6x5) = −30x4
- d/dx(−3x3) = −9x2
- d/dx(x) = 1
5.Differentiate y = −4x5 − 2x3 + 3x2
Answer: dy/dx = −20x4 − 6x2 + 6x
- d/dx(−4x5) = −20x4
- d/dx(−2x3) = −6x2
- d/dx(3x2) = 6x
6.Differentiate y = −5x5 + 9x2 + 2x
Answer: dy/dx = −25x4 + 18x + 2
- d/dx(−5x5) = −25x4
- d/dx(9x2) = 18x
- d/dx(2x) = 2
7.Differentiate y = x5 − 6x − 2
Answer: dy/dx = 5x4 − 6
- d/dx(x5) = 5x4
- d/dx(−6x) = −6
- The derivative of the constant −2 is 0
8.Differentiate y = 3x5 + 7x2 − 7
Answer: dy/dx = 15x4 + 14x
- d/dx(3x5) = 15x4
- d/dx(7x2) = 14x
- The derivative of the constant −7 is 0
9.Differentiate y = 3x5 + 7x3 + 3
Answer: dy/dx = 15x4 + 21x2
- d/dx(3x5) = 15x4
- d/dx(7x3) = 21x2
- The derivative of the constant 3 is 0
10.Differentiate y = 7x5 + 6x3 + 5x
Answer: dy/dx = 35x4 + 18x2 + 5
- d/dx(7x5) = 35x4
- d/dx(6x3) = 18x2
- d/dx(5x) = 5
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