Year 13 Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 2 — 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 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −5x4 − 7x2 + 4x
Answer: dy/dx = −20x3 − 14x + 4
- d/dx(−5x4) = −20x3
- d/dx(−7x2) = −14x
- d/dx(4x) = 4
2.Differentiate y = −6x4 + x3 + x2
Answer: dy/dx = −24x3 + 3x2 + 2x
- d/dx(−6x4) = −24x3
- d/dx(x3) = 3x2
- d/dx(x2) = 2x
3.Differentiate y = −2x5 + x2 + 4x
Answer: dy/dx = −10x4 + 2x + 4
- d/dx(−2x5) = −10x4
- d/dx(x2) = 2x
- d/dx(4x) = 4
4.Differentiate y = x5 + 4x4 − x
Answer: dy/dx = 5x4 + 16x3 − 1
- d/dx(x5) = 5x4
- d/dx(4x4) = 16x3
- d/dx(−x) = −1
5.Differentiate y = 5x5 − 3x2 − 6
Answer: dy/dx = 25x4 − 6x
- d/dx(5x5) = 25x4
- d/dx(−3x2) = −6x
- The derivative of the constant −6 is 0
6.Differentiate y = −7x5 + 8x2 + 8x
Answer: dy/dx = −35x4 + 16x + 8
- d/dx(−7x5) = −35x4
- d/dx(8x2) = 16x
- d/dx(8x) = 8
7.Differentiate y = 2x5 − 6x3 + 7x2
Answer: dy/dx = 10x4 − 18x2 + 14x
- d/dx(2x5) = 10x4
- d/dx(−6x3) = −18x2
- d/dx(7x2) = 14x
8.Differentiate y = 9x5 − 5x4 + 3x
Answer: dy/dx = 45x4 − 20x3 + 3
- d/dx(9x5) = 45x4
- d/dx(−5x4) = −20x3
- d/dx(3x) = 3
9.Differentiate y = −4x4 − 5x2 + 1
Answer: dy/dx = −16x3 − 10x
- d/dx(−4x4) = −16x3
- d/dx(−5x2) = −10x
- The derivative of the constant 1 is 0
10.Differentiate y = 5x4 − 7x3 − 5x2
Answer: dy/dx = 20x3 − 21x2 − 10x
- d/dx(5x4) = 20x3
- d/dx(−7x3) = −21x2
- d/dx(−5x2) = −10x
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