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Grade 12 · Math

Differentiate a power function

Use the power rule on a constant times a positive integer power.

8 generated examples + worked example

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Worked example

Differentiate f(x) = 3x4.

Answer & why

Answer: 12x3

The power rule gives 3 × 4 × x3 = 12x3.

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Try these examples

8 reproducible examples from this math generator. Choose New examples for another set.

Question 1

Differentiate f(x) = 8x4.

  1. 12x3
  2. 8x3
  3. 32x4
  4. 32x3
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 32x3

The power rule gives d/dx(8x4) = 8 × 4 × x4 − 1 = 32x3.

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Question 2

Differentiate f(x) = 8x5.

  1. 8x4
  2. 40x4
  3. 13x4
  4. 41x4
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 40x4

The power rule gives d/dx(8x5) = 8 × 5 × x5 − 1 = 40x4.

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Question 3

Differentiate f(x) = 7x2.

  1. 14x2
  2. 15x1
  3. 9x1
  4. 14x1
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 14x1

The power rule gives d/dx(7x2) = 7 × 2 × x2 − 1 = 14x1.

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Question 4

Differentiate f(x) = 5x2.

  1. 10x1
  2. 11x1
  3. 10x2
  4. 5x1
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 10x1

The power rule gives d/dx(5x2) = 5 × 2 × x2 − 1 = 10x1.

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Question 5

Differentiate f(x) = 6x5.

  1. 6x4
  2. 30x5
  3. 31x4
  4. 30x4
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 30x4

The power rule gives d/dx(6x5) = 6 × 5 × x5 − 1 = 30x4.

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Question 6

Differentiate f(x) = 9x3.

  1. 12x2
  2. 9x2
  3. 27x3
  4. 27x2
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 27x2

The power rule gives d/dx(9x3) = 9 × 3 × x3 − 1 = 27x2.

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Question 7

Differentiate f(x) = 7x5.

  1. 35x4
  2. 7x4
  3. 36x4
  4. 12x4
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 35x4

The power rule gives d/dx(7x5) = 7 × 5 × x5 − 1 = 35x4.

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Question 8

Differentiate f(x) = 3x4.

  1. 12x3
  2. 7x3
  3. 12x4
  4. 3x3
A hint

Multiply by the exponent, then reduce the exponent by one.

Answer & why

Answer: 12x3

The power rule gives d/dx(3x4) = 3 × 4 × x4 − 1 = 12x3.

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