11th Grade Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 2 — 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 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.If f(x) = 5x3 − 5x − 3, find f′(−1).
Answer: f′(−1) = 10
- d/dx(5x3) = 15x2
- d/dx(−5x) = −5
- The derivative of the constant −3 is 0
- f′(x) = 15x2 − 5
- Substitute x = −1: 10
2.If f(x) = 7x6 − 7x3 + 8x, find f′(1).
Answer: f′(1) = 29
- d/dx(7x6) = 42x5
- d/dx(−7x3) = −21x2
- d/dx(8x) = 8
- f′(x) = 42x5 − 21x2 + 8
- Substitute x = 1: 29
3.If f(x) = 3x5 + 9x + 5, find f′(−2).
Answer: f′(−2) = 249
- d/dx(3x5) = 15x4
- d/dx(9x) = 9
- The derivative of the constant 5 is 0
- f′(x) = 15x4 + 9
- Substitute x = −2: 249
4.If f(x) = −2x3 − 5x + 2, find f′(1).
Answer: f′(1) = −11
- d/dx(−2x3) = −6x2
- d/dx(−5x) = −5
- The derivative of the constant 2 is 0
- f′(x) = −6x2 − 5
- Substitute x = 1: −11
5.If f(x) = −2x5 − 6x4 − 3x2, find f′(1).
Answer: f′(1) = −40
- d/dx(−2x5) = −10x4
- d/dx(−6x4) = −24x3
- d/dx(−3x2) = −6x
- f′(x) = −10x4 − 24x3 − 6x
- Substitute x = 1: −40
6.If f(x) = −6x4 + 8x3 + 2, find f′(1).
Answer: f′(1) = 0
- d/dx(−6x4) = −24x3
- d/dx(8x3) = 24x2
- The derivative of the constant 2 is 0
- f′(x) = −24x3 + 24x2
- Substitute x = 1: 0
7.Differentiate y = 8x4 + 7x2 + 8x
Answer: dy/dx = 32x3 + 14x + 8
- d/dx(8x4) = 32x3
- d/dx(7x2) = 14x
- d/dx(8x) = 8
8.If f(x) = 8x5 + x2 + 3x, find f′(−2).
Answer: f′(−2) = 639
- d/dx(8x5) = 40x4
- d/dx(x2) = 2x
- d/dx(3x) = 3
- f′(x) = 40x4 + 2x + 3
- Substitute x = −2: 639
9.If f(x) = −3x6 − 6x + 3, find f′(−2).
Answer: f′(−2) = 570
- d/dx(−3x6) = −18x5
- d/dx(−6x) = −6
- The derivative of the constant 3 is 0
- f′(x) = −18x5 − 6
- Substitute x = −2: 570
10.If f(x) = −6x4 + 3x3 − 2, find f′(2).
Answer: f′(2) = −156
- d/dx(−6x4) = −24x3
- d/dx(3x3) = 9x2
- The derivative of the constant −2 is 0
- f′(x) = −24x3 + 9x2
- Substitute x = 2: −156
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