11th Grade Differentiation (Power Rule) Worksheet — Level 3 — 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 3 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 8x4 − 6x3 − 5x2
Answer: dy/dx = 32x3 − 18x2 − 10x
- d/dx(8x4) = 32x3
- d/dx(−6x3) = −18x2
- d/dx(−5x2) = −10x
2.Differentiate y = 7x5 − 7x4 − 2
Answer: dy/dx = 35x4 − 28x3
- d/dx(7x5) = 35x4
- d/dx(−7x4) = −28x3
- The derivative of the constant −2 is 0
3.Differentiate y = −4x4 − 4x − 2
Answer: dy/dx = −16x3 − 4
- d/dx(−4x4) = −16x3
- d/dx(−4x) = −4
- The derivative of the constant −2 is 0
4.Differentiate y = 2x6 + 3x5 − x
Answer: dy/dx = 12x5 + 15x4 − 1
- d/dx(2x6) = 12x5
- d/dx(3x5) = 15x4
- d/dx(−x) = −1
5.If f(x) = 5x5 − 2x + 8, find f′(−1).
Answer: f′(−1) = 23
- d/dx(5x5) = 25x4
- d/dx(−2x) = −2
- The derivative of the constant 8 is 0
- f′(x) = 25x4 − 2
- Substitute x = −1: 23
6.Differentiate y = 5x6 + 6x3 − 4
Answer: dy/dx = 30x5 + 18x2
- d/dx(5x6) = 30x5
- d/dx(6x3) = 18x2
- The derivative of the constant −4 is 0
7.If f(x) = 8x4 + 5x3 + 4x2, find f′(−1).
Answer: f′(−1) = −25
- d/dx(8x4) = 32x3
- d/dx(5x3) = 15x2
- d/dx(4x2) = 8x
- f′(x) = 32x3 + 15x2 + 8x
- Substitute x = −1: −25
8.Differentiate y = −5x6 + 9x3 − 6x
Answer: dy/dx = −30x5 + 27x2 − 6
- d/dx(−5x6) = −30x5
- d/dx(9x3) = 27x2
- d/dx(−6x) = −6
9.Differentiate y = x5 + x3 − 1
Answer: dy/dx = 5x4 + 3x2
- d/dx(x5) = 5x4
- d/dx(x3) = 3x2
- The derivative of the constant −1 is 0
10.Differentiate y = −x6 − 5x4 + 4
Answer: dy/dx = −6x5 − 20x3
- d/dx(−x6) = −6x5
- d/dx(−5x4) = −20x3
- The derivative of the constant 4 is 0
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