12th Grade Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 2 — Answers
Answer sheet with worked solutions for the 12th Grade calculus worksheet.
Success TutoringWorksheetsAnswer sheet12th Grade · Mathematics · Calculus12th Grade Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 2x5 + 6x4 − 5x2, find f′(−2).
Answer: f′(−2) = −12
- d/dx(2x5) = 10x4
- d/dx(6x4) = 24x3
- d/dx(−5x2) = −10x
- f′(x) = 10x4 + 24x3 − 10x
- Substitute x = −2: −12
2.Differentiate y = −4x4 + 7x2 + 2
Answer: dy/dx = −16x3 + 14x
- d/dx(−4x4) = −16x3
- d/dx(7x2) = 14x
- The derivative of the constant 2 is 0
3.Differentiate y = 3x3 + 5x − 7
Answer: dy/dx = 9x2 + 5
- d/dx(3x3) = 9x2
- d/dx(5x) = 5
- The derivative of the constant −7 is 0
4.If f(x) = −x6 − 2x2 − 1, find f′(−2).
Answer: f′(−2) = 200
- d/dx(−x6) = −6x5
- d/dx(−2x2) = −4x
- The derivative of the constant −1 is 0
- f′(x) = −6x5 − 4x
- Substitute x = −2: 200
5.Differentiate y = −7x6 + 3x3 + 9x2
Answer: dy/dx = −42x5 + 9x2 + 18x
- d/dx(−7x6) = −42x5
- d/dx(3x3) = 9x2
- d/dx(9x2) = 18x
6.If f(x) = x3 + 4x2 + 6x, find f′(−1).
Answer: f′(−1) = 1
- d/dx(x3) = 3x2
- d/dx(4x2) = 8x
- d/dx(6x) = 6
- f′(x) = 3x2 + 8x + 6
- Substitute x = −1: 1
7.Differentiate y = 7x3 − x2 + 2
Answer: dy/dx = 21x2 − 2x
- d/dx(7x3) = 21x2
- d/dx(−x2) = −2x
- The derivative of the constant 2 is 0
8.Differentiate y = 9x6 + 5x5 + x3
Answer: dy/dx = 54x5 + 25x4 + 3x2
- d/dx(9x6) = 54x5
- d/dx(5x5) = 25x4
- d/dx(x3) = 3x2
9.Differentiate y = 4x6 + x5 − 3x
Answer: dy/dx = 24x5 + 5x4 − 3
- d/dx(4x6) = 24x5
- d/dx(x5) = 5x4
- d/dx(−3x) = −3
10.If f(x) = 2x6 − 2x3 − 2x, find f′(1).
Answer: f′(1) = 4
- d/dx(2x6) = 12x5
- d/dx(−2x3) = −6x2
- d/dx(−2x) = −2
- f′(x) = 12x5 − 6x2 − 2
- Substitute x = 1: 4
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