11th Grade Differentiation (Power Rule) Worksheet — Level 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 2x4 − 2x2 − 7
Answer: dy/dx = 8x3 − 4x
- d/dx(2x4) = 8x3
- d/dx(−2x2) = −4x
- The derivative of the constant −7 is 0
2.Differentiate y = −7x5 − 6x4 − x
Answer: dy/dx = −35x4 − 24x3 − 1
- d/dx(−7x5) = −35x4
- d/dx(−6x4) = −24x3
- d/dx(−x) = −1
3.Differentiate y = −7x4 + 3x3 − 7x
Answer: dy/dx = −28x3 + 9x2 − 7
- d/dx(−7x4) = −28x3
- d/dx(3x3) = 9x2
- d/dx(−7x) = −7
4.Differentiate y = 7x5 + 5x2 − 6
Answer: dy/dx = 35x4 + 10x
- d/dx(7x5) = 35x4
- d/dx(5x2) = 10x
- The derivative of the constant −6 is 0
5.Differentiate y = 8x4 + 4x + 1
Answer: dy/dx = 32x3 + 4
- d/dx(8x4) = 32x3
- d/dx(4x) = 4
- The derivative of the constant 1 is 0
6.Differentiate y = x4 + 2x3 + 4
Answer: dy/dx = 4x3 + 6x2
- d/dx(x4) = 4x3
- d/dx(2x3) = 6x2
- The derivative of the constant 4 is 0
7.Differentiate y = −2x4 + 3x3 + x
Answer: dy/dx = −8x3 + 9x2 + 1
- d/dx(−2x4) = −8x3
- d/dx(3x3) = 9x2
- d/dx(x) = 1
8.Differentiate y = 8x3 + 5x + 6
Answer: dy/dx = 24x2 + 5
- d/dx(8x3) = 24x2
- d/dx(5x) = 5
- The derivative of the constant 6 is 0
9.Differentiate y = −3x4 + 8x3 + 6x
Answer: dy/dx = −12x3 + 24x2 + 6
- d/dx(−3x4) = −12x3
- d/dx(8x3) = 24x2
- d/dx(6x) = 6
10.Differentiate y = 6x4 − 3x3 + 6x
Answer: dy/dx = 24x3 − 9x2 + 6
- d/dx(6x4) = 24x3
- d/dx(−3x3) = −9x2
- d/dx(6x) = 6
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