11th Grade Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 2 — 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 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 6x3 + 8x2 + 5x
Answer: dy/dx = 18x2 + 16x + 5
- d/dx(6x3) = 18x2
- d/dx(8x2) = 16x
- d/dx(5x) = 5
2.Differentiate y = −7x3 + 7x + 5
Answer: dy/dx = −21x2 + 7
- d/dx(−7x3) = −21x2
- d/dx(7x) = 7
- The derivative of the constant 5 is 0
3.Differentiate y = −6x5 − 4x − 2
Answer: dy/dx = −30x4 − 4
- d/dx(−6x5) = −30x4
- d/dx(−4x) = −4
- The derivative of the constant −2 is 0
4.Differentiate y = 6x5 − 2x4 + 1
Answer: dy/dx = 30x4 − 8x3
- d/dx(6x5) = 30x4
- d/dx(−2x4) = −8x3
- The derivative of the constant 1 is 0
5.Differentiate y = −4x5 + 5x2 + 4
Answer: dy/dx = −20x4 + 10x
- d/dx(−4x5) = −20x4
- d/dx(5x2) = 10x
- The derivative of the constant 4 is 0
6.Differentiate y = −6x5 + 9x4 + 4x2
Answer: dy/dx = −30x4 + 36x3 + 8x
- d/dx(−6x5) = −30x4
- d/dx(9x4) = 36x3
- d/dx(4x2) = 8x
7.Differentiate y = −5x3 + 6x2 − 2
Answer: dy/dx = −15x2 + 12x
- d/dx(−5x3) = −15x2
- d/dx(6x2) = 12x
- The derivative of the constant −2 is 0
8.Differentiate y = −3x5 + 9x2 + 2x
Answer: dy/dx = −15x4 + 18x + 2
- d/dx(−3x5) = −15x4
- d/dx(9x2) = 18x
- d/dx(2x) = 2
9.Differentiate y = −5x5 + x4 − 4
Answer: dy/dx = −25x4 + 4x3
- d/dx(−5x5) = −25x4
- d/dx(x4) = 4x3
- The derivative of the constant −4 is 0
10.Differentiate y = 2x3 + 5x2 + 3x
Answer: dy/dx = 6x2 + 10x + 3
- d/dx(2x3) = 6x2
- d/dx(5x2) = 10x
- d/dx(3x) = 3
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