12th Grade Differentiation (Power Rule) Worksheet — Level 1 — 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 7x3 − 2
Answer: dy/dx = 21x2
- d/dx(7x3) = 21x2
- The derivative of the constant −2 is 0
2.Differentiate y = −7x2 − 3x
Answer: dy/dx = −14x − 3
- d/dx(−7x2) = −14x
- d/dx(−3x) = −3
3.Differentiate y = 7x3 + 7x2
Answer: dy/dx = 21x2 + 14x
- d/dx(7x3) = 21x2
- d/dx(7x2) = 14x
4.Differentiate y = 4x3 + 3x2
Answer: dy/dx = 12x2 + 6x
- d/dx(4x3) = 12x2
- d/dx(3x2) = 6x
5.Differentiate y = −4x2 − 3x
Answer: dy/dx = −8x − 3
- d/dx(−4x2) = −8x
- d/dx(−3x) = −3
6.Differentiate y = −2x3 − 4x
Answer: dy/dx = −6x2 − 4
- d/dx(−2x3) = −6x2
- d/dx(−4x) = −4
7.Differentiate y = 3x3 − 2
Answer: dy/dx = 9x2
- d/dx(3x3) = 9x2
- The derivative of the constant −2 is 0
8.Differentiate y = −7x2 + 7
Answer: dy/dx = −14x
- d/dx(−7x2) = −14x
- The derivative of the constant 7 is 0
9.Differentiate y = −7x3 − x
Answer: dy/dx = −21x2 − 1
- d/dx(−7x3) = −21x2
- d/dx(−x) = −1
10.Differentiate y = 2x + 8
Answer: dy/dx = 2
- d/dx(2x) = 2
- The derivative of the constant 8 is 0
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