12th Grade Differentiation (Power Rule) Worksheet — Level 2 — 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 2 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 2x5 + 3x4 − 2x2
Answer: dy/dx = 10x4 + 12x3 − 4x
- d/dx(2x5) = 10x4
- d/dx(3x4) = 12x3
- d/dx(−2x2) = −4x
2.Differentiate y = −2x5 + 7x4 − 4x
Answer: dy/dx = −10x4 + 28x3 − 4
- d/dx(−2x5) = −10x4
- d/dx(7x4) = 28x3
- d/dx(−4x) = −4
3.Differentiate y = −2x5 − 7x2 + 2x
Answer: dy/dx = −10x4 − 14x + 2
- d/dx(−2x5) = −10x4
- d/dx(−7x2) = −14x
- d/dx(2x) = 2
4.Differentiate y = −3x5 + 4x − 7
Answer: dy/dx = −15x4 + 4
- d/dx(−3x5) = −15x4
- d/dx(4x) = 4
- The derivative of the constant −7 is 0
5.Differentiate y = −3x5 + 5x4 + 8x2
Answer: dy/dx = −15x4 + 20x3 + 16x
- d/dx(−3x5) = −15x4
- d/dx(5x4) = 20x3
- d/dx(8x2) = 16x
6.Differentiate y = −6x2 − x + 5
Answer: dy/dx = −12x − 1
- d/dx(−6x2) = −12x
- d/dx(−x) = −1
- The derivative of the constant 5 is 0
7.Differentiate y = −5x5 + x4 + x2
Answer: dy/dx = −25x4 + 4x3 + 2x
- d/dx(−5x5) = −25x4
- d/dx(x4) = 4x3
- d/dx(x2) = 2x
8.Differentiate y = −5x5 − 4x4 − 2x3
Answer: dy/dx = −25x4 − 16x3 − 6x2
- d/dx(−5x5) = −25x4
- d/dx(−4x4) = −16x3
- d/dx(−2x3) = −6x2
9.Differentiate y = −x4 − 7x3 − 1
Answer: dy/dx = −4x3 − 21x2
- d/dx(−x4) = −4x3
- d/dx(−7x3) = −21x2
- The derivative of the constant −1 is 0
10.Differentiate y = 7x5 − 7x3 + 2x
Answer: dy/dx = 35x4 − 21x2 + 2
- d/dx(7x5) = 35x4
- d/dx(−7x3) = −21x2
- d/dx(2x) = 2
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