12th Grade Differentiation (Power Rule) Worksheet — Level 2 — Answers
Answer sheet with worked solutions for the 12th Grade calculus worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Calculus12th Grade Differentiation (Power Rule) Worksheet — Level 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 8x4 + 8x3 − x2
Answer: dy/dx = 32x3 + 24x2 − 2x
- d/dx(8x4) = 32x3
- d/dx(8x3) = 24x2
- d/dx(−x2) = −2x
2.Differentiate y = −x5 + 5x4 + 3
Answer: dy/dx = −5x4 + 20x3
- d/dx(−x5) = −5x4
- d/dx(5x4) = 20x3
- The derivative of the constant 3 is 0
3.Differentiate y = −2x2 − 7x + 5
Answer: dy/dx = −4x − 7
- d/dx(−2x2) = −4x
- d/dx(−7x) = −7
- The derivative of the constant 5 is 0
4.Differentiate y = −3x4 + 8x − 1
Answer: dy/dx = −12x3 + 8
- d/dx(−3x4) = −12x3
- d/dx(8x) = 8
- The derivative of the constant −1 is 0
5.Differentiate y = x5 − 7x2 − 7x
Answer: dy/dx = 5x4 − 14x − 7
- d/dx(x5) = 5x4
- d/dx(−7x2) = −14x
- d/dx(−7x) = −7
6.Differentiate y = 6x5 + 2x2 − 1
Answer: dy/dx = 30x4 + 4x
- d/dx(6x5) = 30x4
- d/dx(2x2) = 4x
- The derivative of the constant −1 is 0
7.Differentiate y = −5x5 + 6x4 + 8
Answer: dy/dx = −25x4 + 24x3
- d/dx(−5x5) = −25x4
- d/dx(6x4) = 24x3
- The derivative of the constant 8 is 0
8.Differentiate y = 8x4 + 3x2 − 3
Answer: dy/dx = 32x3 + 6x
- d/dx(8x4) = 32x3
- d/dx(3x2) = 6x
- The derivative of the constant −3 is 0
9.Differentiate y = −2x4 + 5x3 − 1
Answer: dy/dx = −8x3 + 15x2
- d/dx(−2x4) = −8x3
- d/dx(5x3) = 15x2
- The derivative of the constant −1 is 0
10.Differentiate y = 3x3 + 7x2 + 7x
Answer: dy/dx = 9x2 + 14x + 7
- d/dx(3x3) = 9x2
- d/dx(7x2) = 14x
- d/dx(7x) = 7
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