11th Grade Differentiation (Power Rule) Worksheet — Level 2 — Practice Set 3 — 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 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 5x5 + x4 + 3x3
Answer: dy/dx = 25x4 + 4x3 + 9x2
- d/dx(5x5) = 25x4
- d/dx(x4) = 4x3
- d/dx(3x3) = 9x2
2.Differentiate y = 8x4 − 6x3 + 3x2
Answer: dy/dx = 32x3 − 18x2 + 6x
- d/dx(8x4) = 32x3
- d/dx(−6x3) = −18x2
- d/dx(3x2) = 6x
3.Differentiate y = 2x4 − 7x3 + 8x2
Answer: dy/dx = 8x3 − 21x2 + 16x
- d/dx(2x4) = 8x3
- d/dx(−7x3) = −21x2
- d/dx(8x2) = 16x
4.Differentiate y = −6x4 + 4x3 − x2
Answer: dy/dx = −24x3 + 12x2 − 2x
- d/dx(−6x4) = −24x3
- d/dx(4x3) = 12x2
- d/dx(−x2) = −2x
5.Differentiate y = 9x5 + 7x + 1
Answer: dy/dx = 45x4 + 7
- d/dx(9x5) = 45x4
- d/dx(7x) = 7
- The derivative of the constant 1 is 0
6.Differentiate y = 9x5 + 4x2 + 3
Answer: dy/dx = 45x4 + 8x
- d/dx(9x5) = 45x4
- d/dx(4x2) = 8x
- The derivative of the constant 3 is 0
7.Differentiate y = −2x4 + 6x2 + 9
Answer: dy/dx = −8x3 + 12x
- d/dx(−2x4) = −8x3
- d/dx(6x2) = 12x
- The derivative of the constant 9 is 0
8.Differentiate y = −6x5 + 5x4 + 4x
Answer: dy/dx = −30x4 + 20x3 + 4
- d/dx(−6x5) = −30x4
- d/dx(5x4) = 20x3
- d/dx(4x) = 4
9.Differentiate y = x5 − 2x + 9
Answer: dy/dx = 5x4 − 2
- d/dx(x5) = 5x4
- d/dx(−2x) = −2
- The derivative of the constant 9 is 0
10.Differentiate y = 9x5 + 2x3 − 5x2
Answer: dy/dx = 45x4 + 6x2 − 10x
- d/dx(9x5) = 45x4
- d/dx(2x3) = 6x2
- d/dx(−5x2) = −10x
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