12th Grade Differentiation (Power Rule) Worksheet — Level 2 — Practice 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 2 — Practice Set 2 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 2x4 + x3 − 6
Answer: dy/dx = 8x3 + 3x2
- d/dx(2x4) = 8x3
- d/dx(x3) = 3x2
- The derivative of the constant −6 is 0
2.Differentiate y = x5 + x4 + 3x
Answer: dy/dx = 5x4 + 4x3 + 3
- d/dx(x5) = 5x4
- d/dx(x4) = 4x3
- d/dx(3x) = 3
3.Differentiate y = 7x4 + x2 − 6
Answer: dy/dx = 28x3 + 2x
- d/dx(7x4) = 28x3
- d/dx(x2) = 2x
- The derivative of the constant −6 is 0
4.Differentiate y = 5x4 − 6x2 + 6x
Answer: dy/dx = 20x3 − 12x + 6
- d/dx(5x4) = 20x3
- d/dx(−6x2) = −12x
- d/dx(6x) = 6
5.Differentiate y = −x5 + 2x4 − 5
Answer: dy/dx = −5x4 + 8x3
- d/dx(−x5) = −5x4
- d/dx(2x4) = 8x3
- The derivative of the constant −5 is 0
6.Differentiate y = 9x5 + 3x4 + 6x
Answer: dy/dx = 45x4 + 12x3 + 6
- d/dx(9x5) = 45x4
- d/dx(3x4) = 12x3
- d/dx(6x) = 6
7.Differentiate y = −7x4 + 6x3 + 3
Answer: dy/dx = −28x3 + 18x2
- d/dx(−7x4) = −28x3
- d/dx(6x3) = 18x2
- The derivative of the constant 3 is 0
8.Differentiate y = −x5 − 3x4 − 5x
Answer: dy/dx = −5x4 − 12x3 − 5
- d/dx(−x5) = −5x4
- d/dx(−3x4) = −12x3
- d/dx(−5x) = −5
9.Differentiate y = −4x5 − 2x2 + 7x
Answer: dy/dx = −20x4 − 4x + 7
- d/dx(−4x5) = −20x4
- d/dx(−2x2) = −4x
- d/dx(7x) = 7
10.Differentiate y = 8x5 − 5x3 − x2
Answer: dy/dx = 40x4 − 15x2 − 2x
- d/dx(8x5) = 40x4
- d/dx(−5x3) = −15x2
- d/dx(−x2) = −2x
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