11th Grade Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 4 — Answers
Answer sheet with worked solutions for the 11th Grade calculus worksheet.
Success TutoringWorksheetsAnswer sheet11th Grade · Mathematics · Calculus11th Grade Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 9x5 + 9x3 + 9x
Answer: dy/dx = 45x4 + 27x2 + 9
- d/dx(9x5) = 45x4
- d/dx(9x3) = 27x2
- d/dx(9x) = 9
2.Differentiate y = 9x4 − 6x3 − x
Answer: dy/dx = 36x3 − 18x2 − 1
- d/dx(9x4) = 36x3
- d/dx(−6x3) = −18x2
- d/dx(−x) = −1
3.Differentiate y = 5x4 + x − 7
Answer: dy/dx = 20x3 + 1
- d/dx(5x4) = 20x3
- d/dx(x) = 1
- The derivative of the constant −7 is 0
4.Differentiate y = −6x5 − 6x2 − 5x
Answer: dy/dx = −30x4 − 12x − 5
- d/dx(−6x5) = −30x4
- d/dx(−6x2) = −12x
- d/dx(−5x) = −5
5.Differentiate y = x5 − 2x − 7
Answer: dy/dx = 5x4 − 2
- d/dx(x5) = 5x4
- d/dx(−2x) = −2
- The derivative of the constant −7 is 0
6.Differentiate y = −2x4 − x3 − 2x2
Answer: dy/dx = −8x3 − 3x2 − 4x
- d/dx(−2x4) = −8x3
- d/dx(−x3) = −3x2
- d/dx(−2x2) = −4x
7.Differentiate y = 4x2 + 9x − 3
Answer: dy/dx = 8x + 9
- d/dx(4x2) = 8x
- d/dx(9x) = 9
- The derivative of the constant −3 is 0
8.Differentiate y = −5x3 + 6x + 4
Answer: dy/dx = −15x2 + 6
- d/dx(−5x3) = −15x2
- d/dx(6x) = 6
- The derivative of the constant 4 is 0
9.Differentiate y = 4x3 + 6x2 − 7x
Answer: dy/dx = 12x2 + 12x − 7
- d/dx(4x3) = 12x2
- d/dx(6x2) = 12x
- d/dx(−7x) = −7
10.Differentiate y = 6x5 + 9x3 − 2x
Answer: dy/dx = 30x4 + 27x2 − 2
- d/dx(6x5) = 30x4
- d/dx(9x3) = 27x2
- d/dx(−2x) = −2
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