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Question 12

MEDIUM

What is the derivative of f(x)=x3f(x) = x^3?

Right triangle diagram
Practice diagram rendered from a question-linked asset.

Differentiate using the power rule:

f(x)=x3Rightarrowf′(x)=3x2f(x) = x^3 \\Rightarrow f'(x) = 3x^2

Derivative sketch

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Question 12 of 24

AI explanation

High confidence

Great job — differentiating x3x^3 yields 3x23x^2 by multiplying the exponent and subtracting one.

Key points

  • Apply the power rule
  • Reduce the exponent by one
  • Simplify coefficients

Steps

  1. Identify the exponent (3)
  2. Multiply by the exponent
  3. Subtract one from the exponent
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Question 12 of 24

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