11th Grade Differentiation (Power Rule) Worksheet — Level 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 5x6 + 2x + 4, find f′(2).
Answer: f′(2) = 962
- d/dx(5x6) = 30x5
- d/dx(2x) = 2
- The derivative of the constant 4 is 0
- f′(x) = 30x5 + 2
- Substitute x = 2: 962
2.If f(x) = −2x5 + x3 − 6, find f′(1).
Answer: f′(1) = −7
- d/dx(−2x5) = −10x4
- d/dx(x3) = 3x2
- The derivative of the constant −6 is 0
- f′(x) = −10x4 + 3x2
- Substitute x = 1: −7
3.If f(x) = 9x6 − 7x2 + 4, find f′(2).
Answer: f′(2) = 1700
- d/dx(9x6) = 54x5
- d/dx(−7x2) = −14x
- The derivative of the constant 4 is 0
- f′(x) = 54x5 − 14x
- Substitute x = 2: 1700
4.Differentiate y = 2x5 + 3x4 − 2x
Answer: dy/dx = 10x4 + 12x3 − 2
- d/dx(2x5) = 10x4
- d/dx(3x4) = 12x3
- d/dx(−2x) = −2
5.If f(x) = −4x5 + 7x4 + 9x, find f′(−2).
Answer: f′(−2) = −535
- d/dx(−4x5) = −20x4
- d/dx(7x4) = 28x3
- d/dx(9x) = 9
- f′(x) = −20x4 + 28x3 + 9
- Substitute x = −2: −535
6.Differentiate y = −4x4 + 2x3 − 5x2
Answer: dy/dx = −16x3 + 6x2 − 10x
- d/dx(−4x4) = −16x3
- d/dx(2x3) = 6x2
- d/dx(−5x2) = −10x
7.If f(x) = 9x5 + 6x3 + x2, find f′(−1).
Answer: f′(−1) = 61
- d/dx(9x5) = 45x4
- d/dx(6x3) = 18x2
- d/dx(x2) = 2x
- f′(x) = 45x4 + 18x2 + 2x
- Substitute x = −1: 61
8.If f(x) = 7x5 + x3 − 2x2, find f′(2).
Answer: f′(2) = 564
- d/dx(7x5) = 35x4
- d/dx(x3) = 3x2
- d/dx(−2x2) = −4x
- f′(x) = 35x4 + 3x2 − 4x
- Substitute x = 2: 564
9.Differentiate y = 5x6 − 2x5 − 7x2
Answer: dy/dx = 30x5 − 10x4 − 14x
- d/dx(5x6) = 30x5
- d/dx(−2x5) = −10x4
- d/dx(−7x2) = −14x
10.Differentiate y = −7x6 − 7x5 + x3
Answer: dy/dx = −42x5 − 35x4 + 3x2
- d/dx(−7x6) = −42x5
- d/dx(−7x5) = −35x4
- d/dx(x3) = 3x2
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