12th Grade Differentiation (Power Rule) Worksheet — Level 2 — 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 2 — Practice Set 4 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 6x5 + 5x2 + 6
Answer: dy/dx = 30x4 + 10x
- d/dx(6x5) = 30x4
- d/dx(5x2) = 10x
- The derivative of the constant 6 is 0
2.Differentiate y = 9x3 + 9x2 + x
Answer: dy/dx = 27x2 + 18x + 1
- d/dx(9x3) = 27x2
- d/dx(9x2) = 18x
- d/dx(x) = 1
3.Differentiate y = 8x4 + x2 − 6
Answer: dy/dx = 32x3 + 2x
- d/dx(8x4) = 32x3
- d/dx(x2) = 2x
- The derivative of the constant −6 is 0
4.Differentiate y = −2x5 + 7x4 + 5x
Answer: dy/dx = −10x4 + 28x3 + 5
- d/dx(−2x5) = −10x4
- d/dx(7x4) = 28x3
- d/dx(5x) = 5
5.Differentiate y = x5 − x3 − 3
Answer: dy/dx = 5x4 − 3x2
- d/dx(x5) = 5x4
- d/dx(−x3) = −3x2
- The derivative of the constant −3 is 0
6.Differentiate y = 4x4 − 6x + 4
Answer: dy/dx = 16x3 − 6
- d/dx(4x4) = 16x3
- d/dx(−6x) = −6
- The derivative of the constant 4 is 0
7.Differentiate y = −3x4 + 5x2 + x
Answer: dy/dx = −12x3 + 10x + 1
- d/dx(−3x4) = −12x3
- d/dx(5x2) = 10x
- d/dx(x) = 1
8.Differentiate y = 4x3 − 6x2 + 9
Answer: dy/dx = 12x2 − 12x
- d/dx(4x3) = 12x2
- d/dx(−6x2) = −12x
- The derivative of the constant 9 is 0
9.Differentiate y = 8x5 − 3x4 − 5
Answer: dy/dx = 40x4 − 12x3
- d/dx(8x5) = 40x4
- d/dx(−3x4) = −12x3
- The derivative of the constant −5 is 0
10.Differentiate y = 5x2 + 5x + 4
Answer: dy/dx = 10x + 5
- d/dx(5x2) = 10x
- d/dx(5x) = 5
- The derivative of the constant 4 is 0
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