11th Grade Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −x6 − 6x4 + 3x2
Answer: dy/dx = −6x5 − 24x3 + 6x
- d/dx(−x6) = −6x5
- d/dx(−6x4) = −24x3
- d/dx(3x2) = 6x
2.If f(x) = 8x4 + 7x2 + 8, find f′(−1).
Answer: f′(−1) = −46
- d/dx(8x4) = 32x3
- d/dx(7x2) = 14x
- The derivative of the constant 8 is 0
- f′(x) = 32x3 + 14x
- Substitute x = −1: −46
3.Differentiate y = −7x5 − 2x + 5
Answer: dy/dx = −35x4 − 2
- d/dx(−7x5) = −35x4
- d/dx(−2x) = −2
- The derivative of the constant 5 is 0
4.If f(x) = −5x6 + 8x + 4, find f′(1).
Answer: f′(1) = −22
- d/dx(−5x6) = −30x5
- d/dx(8x) = 8
- The derivative of the constant 4 is 0
- f′(x) = −30x5 + 8
- Substitute x = 1: −22
5.Differentiate y = 6x6 + 8x4 − x3
Answer: dy/dx = 36x5 + 32x3 − 3x2
- d/dx(6x6) = 36x5
- d/dx(8x4) = 32x3
- d/dx(−x3) = −3x2
6.If f(x) = 4x5 + 4x − 2, find f′(1).
Answer: f′(1) = 24
- d/dx(4x5) = 20x4
- d/dx(4x) = 4
- The derivative of the constant −2 is 0
- f′(x) = 20x4 + 4
- Substitute x = 1: 24
7.Differentiate y = −7x6 + 4x4 + 5x2
Answer: dy/dx = −42x5 + 16x3 + 10x
- d/dx(−7x6) = −42x5
- d/dx(4x4) = 16x3
- d/dx(5x2) = 10x
8.If f(x) = 2x5 + 9x3 − 3x2, find f′(2).
Answer: f′(2) = 256
- d/dx(2x5) = 10x4
- d/dx(9x3) = 27x2
- d/dx(−3x2) = −6x
- f′(x) = 10x4 + 27x2 − 6x
- Substitute x = 2: 256
9.Differentiate y = 6x6 + 2x + 4
Answer: dy/dx = 36x5 + 2
- d/dx(6x6) = 36x5
- d/dx(2x) = 2
- The derivative of the constant 4 is 0
10.Differentiate y = −x6 + 2x5 + 8x4
Answer: dy/dx = −6x5 + 10x4 + 32x3
- d/dx(−x6) = −6x5
- d/dx(2x5) = 10x4
- d/dx(8x4) = 32x3
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