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What is the derivative of x^3?

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Question: What is the derivative of x^3?

Options:

  1. 3x^2
  2. 2x^3
  3. x^2
  4. 3x

Correct Answer: 3x^2

Solution: 

The derivative of x^3 is 3x^2.

What is the derivative of x^3?

Practice Questions

Q1
What is the derivative of x^3?
  1. 3x^2
  2. 2x^3
  3. x^2
  4. 3x

Questions & Step-by-Step Solutions

What is the derivative of x^3?
  • Step 1: Understand that the derivative measures how a function changes as its input changes.
  • Step 2: Identify the function we are working with, which is x^3.
  • Step 3: Use the power rule for derivatives, which states that if you have x^n, the derivative is n*x^(n-1).
  • Step 4: In our case, n is 3 because we have x^3.
  • Step 5: Apply the power rule: Multiply the exponent (3) by the base (x) raised to the exponent minus one (3-1).
  • Step 6: Calculate: 3 * x^(3-1) = 3 * x^2.
  • Step 7: Write the final answer: The derivative of x^3 is 3x^2.
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