Year 13 Differentiation (Power Rule) Worksheet — Level 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 8x5 − 3x3 − 5
Answer: dy/dx = 40x4 − 9x2
- d/dx(8x5) = 40x4
- d/dx(−3x3) = −9x2
- The derivative of the constant −5 is 0
2.Differentiate y = −3x5 − 5x4 + 7x2
Answer: dy/dx = −15x4 − 20x3 + 14x
- d/dx(−3x5) = −15x4
- d/dx(−5x4) = −20x3
- d/dx(7x2) = 14x
3.Differentiate y = 4x4 − 6x3 − 5
Answer: dy/dx = 16x3 − 18x2
- d/dx(4x4) = 16x3
- d/dx(−6x3) = −18x2
- The derivative of the constant −5 is 0
4.Differentiate y = 8x5 + 4x − 7
Answer: dy/dx = 40x4 + 4
- d/dx(8x5) = 40x4
- d/dx(4x) = 4
- The derivative of the constant −7 is 0
5.Differentiate y = −x5 − 7x3 + 9x2
Answer: dy/dx = −5x4 − 21x2 + 18x
- d/dx(−x5) = −5x4
- d/dx(−7x3) = −21x2
- d/dx(9x2) = 18x
6.Differentiate y = 9x4 + 3x3 + x
Answer: dy/dx = 36x3 + 9x2 + 1
- d/dx(9x4) = 36x3
- d/dx(3x3) = 9x2
- d/dx(x) = 1
7.Differentiate y = 8x5 + 8x4 + 9
Answer: dy/dx = 40x4 + 32x3
- d/dx(8x5) = 40x4
- d/dx(8x4) = 32x3
- The derivative of the constant 9 is 0
8.Differentiate y = −6x4 − 3x3 − 2x
Answer: dy/dx = −24x3 − 9x2 − 2
- d/dx(−6x4) = −24x3
- d/dx(−3x3) = −9x2
- d/dx(−2x) = −2
9.Differentiate y = 6x4 − 4x + 4
Answer: dy/dx = 24x3 − 4
- d/dx(6x4) = 24x3
- d/dx(−4x) = −4
- The derivative of the constant 4 is 0
10.Differentiate y = −2x5 − 3x4 − 6x
Answer: dy/dx = −10x4 − 12x3 − 6
- d/dx(−2x5) = −10x4
- d/dx(−3x4) = −12x3
- d/dx(−6x) = −6
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