12th Grade Differentiation (Power Rule) Worksheet — Level 1 — 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 1 — Practice Set 3 — Answers
Use the power rule: d/dx(axⁿ) = naxⁿ⁻¹.
1.Differentiate y = 5x3 + 7x2
Answer: dy/dx = 15x2 + 14x
- d/dx(5x3) = 15x2
- d/dx(7x2) = 14x
2.Differentiate y = 8x2 − 2x
Answer: dy/dx = 16x − 2
- d/dx(8x2) = 16x
- d/dx(−2x) = −2
3.Differentiate y = 4x3 + 3
Answer: dy/dx = 12x2
- d/dx(4x3) = 12x2
- The derivative of the constant 3 is 0
4.Differentiate y = 9x2 + 5x
Answer: dy/dx = 18x + 5
- d/dx(9x2) = 18x
- d/dx(5x) = 5
5.Differentiate y = −7x − 2
Answer: dy/dx = −7
- d/dx(−7x) = −7
- The derivative of the constant −2 is 0
6.Differentiate y = 3x3 − 4x2
Answer: dy/dx = 9x2 − 8x
- d/dx(3x3) = 9x2
- d/dx(−4x2) = −8x
7.Differentiate y = 8x2 + x
Answer: dy/dx = 16x + 1
- d/dx(8x2) = 16x
- d/dx(x) = 1
8.Differentiate y = 8x2 + 6
Answer: dy/dx = 16x
- d/dx(8x2) = 16x
- The derivative of the constant 6 is 0
9.Differentiate y = −7x3 − 4
Answer: dy/dx = −21x2
- d/dx(−7x3) = −21x2
- The derivative of the constant −4 is 0
10.Differentiate y = 9x3 + 3x2
Answer: dy/dx = 27x2 + 6x
- d/dx(9x3) = 27x2
- d/dx(3x2) = 6x
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