12th Grade Differentiation (Power Rule) Worksheet — Level 3 (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 (Set 2) — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 7x5 + 2x4 + 2, find f′(2).
Answer: f′(2) = 624
- d/dx(7x5) = 35x4
- d/dx(2x4) = 8x3
- The derivative of the constant 2 is 0
- f′(x) = 35x4 + 8x3
- Substitute x = 2: 624
2.If f(x) = −3x6 + 8x5 − 4x2, find f′(−1).
Answer: f′(−1) = 66
- d/dx(−3x6) = −18x5
- d/dx(8x5) = 40x4
- d/dx(−4x2) = −8x
- f′(x) = −18x5 + 40x4 − 8x
- Substitute x = −1: 66
3.If f(x) = 3x4 + 8x2 + 9x, find f′(−1).
Answer: f′(−1) = −19
- d/dx(3x4) = 12x3
- d/dx(8x2) = 16x
- d/dx(9x) = 9
- f′(x) = 12x3 + 16x + 9
- Substitute x = −1: −19
4.If f(x) = −4x6 + 2x3 + 6, find f′(−1).
Answer: f′(−1) = 30
- d/dx(−4x6) = −24x5
- d/dx(2x3) = 6x2
- The derivative of the constant 6 is 0
- f′(x) = −24x5 + 6x2
- Substitute x = −1: 30
5.Differentiate y = −2x3 − 7x − 4
Answer: dy/dx = −6x2 − 7
- d/dx(−2x3) = −6x2
- d/dx(−7x) = −7
- The derivative of the constant −4 is 0
6.If f(x) = 7x5 + 6x3 + 4x, find f′(−1).
Answer: f′(−1) = 57
- d/dx(7x5) = 35x4
- d/dx(6x3) = 18x2
- d/dx(4x) = 4
- f′(x) = 35x4 + 18x2 + 4
- Substitute x = −1: 57
7.Differentiate y = 7x6 + x5 + 1
Answer: dy/dx = 42x5 + 5x4
- d/dx(7x6) = 42x5
- d/dx(x5) = 5x4
- The derivative of the constant 1 is 0
8.If f(x) = −x3 − 2x + 1, find f′(1).
Answer: f′(1) = −5
- d/dx(−x3) = −3x2
- d/dx(−2x) = −2
- The derivative of the constant 1 is 0
- f′(x) = −3x2 − 2
- Substitute x = 1: −5
9.If f(x) = 4x5 − 2x2 − 7, find f′(2).
Answer: f′(2) = 312
- d/dx(4x5) = 20x4
- d/dx(−2x2) = −4x
- The derivative of the constant −7 is 0
- f′(x) = 20x4 − 4x
- Substitute x = 2: 312
10.Differentiate y = −4x6 − x4 + 4
Answer: dy/dx = −24x5 − 4x3
- d/dx(−4x6) = −24x5
- d/dx(−x4) = −4x3
- The derivative of the constant 4 is 0
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