12th Grade Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 4 — Answers
Answer sheet with worked solutions for the 12th Grade calculus worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Calculus12th Grade Differentiation (Power Rule) Worksheet — Level 1 — Practice Set 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 3x + 8
Answer: dy/dx = 3
- d/dx(3x) = 3
- The derivative of the constant 8 is 0
2.Differentiate y = 2x3 − 6x
Answer: dy/dx = 6x2 − 6
- d/dx(2x3) = 6x2
- d/dx(−6x) = −6
3.Differentiate y = −2x3 − 1
Answer: dy/dx = −6x2
- d/dx(−2x3) = −6x2
- The derivative of the constant −1 is 0
4.Differentiate y = 3x2 − 6x
Answer: dy/dx = 6x − 6
- d/dx(3x2) = 6x
- d/dx(−6x) = −6
5.Differentiate y = 5x3 + 2x2
Answer: dy/dx = 15x2 + 4x
- d/dx(5x3) = 15x2
- d/dx(2x2) = 4x
6.Differentiate y = 5x2 + 5x
Answer: dy/dx = 10x + 5
- d/dx(5x2) = 10x
- d/dx(5x) = 5
7.Differentiate y = −x3 − x
Answer: dy/dx = −3x2 − 1
- d/dx(−x3) = −3x2
- d/dx(−x) = −1
8.Differentiate y = 7x3 + 5x
Answer: dy/dx = 21x2 + 5
- d/dx(7x3) = 21x2
- d/dx(5x) = 5
9.Differentiate y = 7x2 − 2
Answer: dy/dx = 14x
- d/dx(7x2) = 14x
- The derivative of the constant −2 is 0
10.Differentiate y = −3x2 − 5
Answer: dy/dx = −6x
- d/dx(−3x2) = −6x
- The derivative of the constant −5 is 0
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