12th Grade Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 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 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 4x4 + 9x2 + 8x, find f′(−1).
Answer: f′(−1) = −26
- d/dx(4x4) = 16x3
- d/dx(9x2) = 18x
- d/dx(8x) = 8
- f′(x) = 16x3 + 18x + 8
- Substitute x = −1: −26
2.If f(x) = 3x6 + 9x4 + 9x2, find f′(−2).
Answer: f′(−2) = −900
- d/dx(3x6) = 18x5
- d/dx(9x4) = 36x3
- d/dx(9x2) = 18x
- f′(x) = 18x5 + 36x3 + 18x
- Substitute x = −2: −900
3.Differentiate y = 5x5 − 2x4 + 4x
Answer: dy/dx = 25x4 − 8x3 + 4
- d/dx(5x5) = 25x4
- d/dx(−2x4) = −8x3
- d/dx(4x) = 4
4.If f(x) = −4x5 + 9x4 − 4x3, find f′(2).
Answer: f′(2) = −80
- d/dx(−4x5) = −20x4
- d/dx(9x4) = 36x3
- d/dx(−4x3) = −12x2
- f′(x) = −20x4 + 36x3 − 12x2
- Substitute x = 2: −80
5.Differentiate y = 6x5 − 2x2 + 5x
Answer: dy/dx = 30x4 − 4x + 5
- d/dx(6x5) = 30x4
- d/dx(−2x2) = −4x
- d/dx(5x) = 5
6.Differentiate y = −3x3 + 3x + 2
Answer: dy/dx = −9x2 + 3
- d/dx(−3x3) = −9x2
- d/dx(3x) = 3
- The derivative of the constant 2 is 0
7.Differentiate y = −2x6 + 3x4 − 3x2
Answer: dy/dx = −12x5 + 12x3 − 6x
- d/dx(−2x6) = −12x5
- d/dx(3x4) = 12x3
- d/dx(−3x2) = −6x
8.If f(x) = −x5 − 5x4 − 5x3, find f′(1).
Answer: f′(1) = −40
- d/dx(−x5) = −5x4
- d/dx(−5x4) = −20x3
- d/dx(−5x3) = −15x2
- f′(x) = −5x4 − 20x3 − 15x2
- Substitute x = 1: −40
9.Differentiate y = 4x6 − x5 + 9
Answer: dy/dx = 24x5 − 5x4
- d/dx(4x6) = 24x5
- d/dx(−x5) = −5x4
- The derivative of the constant 9 is 0
10.Differentiate y = 7x6 − 2x4 + 4x3
Answer: dy/dx = 42x5 − 8x3 + 12x2
- d/dx(7x6) = 42x5
- d/dx(−2x4) = −8x3
- d/dx(4x3) = 12x2
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