12th Grade Differentiation (Power Rule) Worksheet — Level 3 — 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 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = −x6 + 7x5 − 1
Answer: dy/dx = −6x5 + 35x4
- d/dx(−x6) = −6x5
- d/dx(7x5) = 35x4
- The derivative of the constant −1 is 0
2.Differentiate y = 7x5 + 5x − 7
Answer: dy/dx = 35x4 + 5
- d/dx(7x5) = 35x4
- d/dx(5x) = 5
- The derivative of the constant −7 is 0
3.If f(x) = −3x4 − x2 + 1, find f′(2).
Answer: f′(2) = −100
- d/dx(−3x4) = −12x3
- d/dx(−x2) = −2x
- The derivative of the constant 1 is 0
- f′(x) = −12x3 − 2x
- Substitute x = 2: −100
4.If f(x) = 4x5 + 5x4 + 9x3, find f′(1).
Answer: f′(1) = 67
- d/dx(4x5) = 20x4
- d/dx(5x4) = 20x3
- d/dx(9x3) = 27x2
- f′(x) = 20x4 + 20x3 + 27x2
- Substitute x = 1: 67
5.If f(x) = −4x6 + 2x3 − 1, find f′(−1).
Answer: f′(−1) = 30
- d/dx(−4x6) = −24x5
- d/dx(2x3) = 6x2
- The derivative of the constant −1 is 0
- f′(x) = −24x5 + 6x2
- Substitute x = −1: 30
6.If f(x) = 5x5 − 6x2 − 6x, find f′(2).
Answer: f′(2) = 370
- d/dx(5x5) = 25x4
- d/dx(−6x2) = −12x
- d/dx(−6x) = −6
- f′(x) = 25x4 − 12x − 6
- Substitute x = 2: 370
7.If f(x) = −2x5 + 5x3 − 1, find f′(2).
Answer: f′(2) = −100
- d/dx(−2x5) = −10x4
- d/dx(5x3) = 15x2
- The derivative of the constant −1 is 0
- f′(x) = −10x4 + 15x2
- Substitute x = 2: −100
8.If f(x) = 2x5 + 6x3 + 4, find f′(2).
Answer: f′(2) = 232
- d/dx(2x5) = 10x4
- d/dx(6x3) = 18x2
- The derivative of the constant 4 is 0
- f′(x) = 10x4 + 18x2
- Substitute x = 2: 232
9.Differentiate y = −6x6 − 3x4 + 7x3
Answer: dy/dx = −36x5 − 12x3 + 21x2
- d/dx(−6x6) = −36x5
- d/dx(−3x4) = −12x3
- d/dx(7x3) = 21x2
10.If f(x) = −6x6 + 6x3 + 5, find f′(1).
Answer: f′(1) = −18
- d/dx(−6x6) = −36x5
- d/dx(6x3) = 18x2
- The derivative of the constant 5 is 0
- f′(x) = −36x5 + 18x2
- Substitute x = 1: −18
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