12th Grade Differentiation (Power Rule) Worksheet — Level 3 — Practice Set 4 — 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 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 9x6 − 7x4 + x
Answer: dy/dx = 54x5 − 28x3 + 1
- d/dx(9x6) = 54x5
- d/dx(−7x4) = −28x3
- d/dx(x) = 1
2.If f(x) = 4x4 − 7x2 + 7, find f′(1).
Answer: f′(1) = 2
- d/dx(4x4) = 16x3
- d/dx(−7x2) = −14x
- The derivative of the constant 7 is 0
- f′(x) = 16x3 − 14x
- Substitute x = 1: 2
3.Differentiate y = 9x3 + 4x2 + 2x
Answer: dy/dx = 27x2 + 8x + 2
- d/dx(9x3) = 27x2
- d/dx(4x2) = 8x
- d/dx(2x) = 2
4.If f(x) = 5x6 − 3x4 + 6x2, find f′(−2).
Answer: f′(−2) = −888
- d/dx(5x6) = 30x5
- d/dx(−3x4) = −12x3
- d/dx(6x2) = 12x
- f′(x) = 30x5 − 12x3 + 12x
- Substitute x = −2: −888
5.Differentiate y = 2x6 − 4x3 + 4x2
Answer: dy/dx = 12x5 − 12x2 + 8x
- d/dx(2x6) = 12x5
- d/dx(−4x3) = −12x2
- d/dx(4x2) = 8x
6.If f(x) = −5x6 + 5x3 + 6x, find f′(1).
Answer: f′(1) = −9
- d/dx(−5x6) = −30x5
- d/dx(5x3) = 15x2
- d/dx(6x) = 6
- f′(x) = −30x5 + 15x2 + 6
- Substitute x = 1: −9
7.Differentiate y = 7x6 + 8x5 − 6x4
Answer: dy/dx = 42x5 + 40x4 − 24x3
- d/dx(7x6) = 42x5
- d/dx(8x5) = 40x4
- d/dx(−6x4) = −24x3
8.Differentiate y = 7x5 + 7x4 + 8x
Answer: dy/dx = 35x4 + 28x3 + 8
- d/dx(7x5) = 35x4
- d/dx(7x4) = 28x3
- d/dx(8x) = 8
9.Differentiate y = 9x5 + 2x + 6
Answer: dy/dx = 45x4 + 2
- d/dx(9x5) = 45x4
- d/dx(2x) = 2
- The derivative of the constant 6 is 0
10.If f(x) = −x6 − 6x2 − 1, find f′(2).
Answer: f′(2) = −216
- d/dx(−x6) = −6x5
- d/dx(−6x2) = −12x
- The derivative of the constant −1 is 0
- f′(x) = −6x5 − 12x
- Substitute x = 2: −216
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