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What is the derivative of f(x) = x^2 at x = 3?

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Question: What is the derivative of f(x) = x^2 at x = 3?

Options:

  1. 3
  2. 6
  3. 9
  4. 12

Correct Answer: 6

Solution: 

f\'(x) = 2x; f\'(3) = 2*3 = 6.

What is the derivative of f(x) = x^2 at x = 3?

Practice Questions

Q1
What is the derivative of f(x) = x^2 at x = 3?
  1. 3
  2. 6
  3. 9
  4. 12

Questions & Step-by-Step Solutions

What is the derivative of f(x) = x^2 at x = 3?
  • Step 1: Identify the function we want to find the derivative of, which is f(x) = x^2.
  • Step 2: Use the power rule for derivatives. The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).
  • Step 3: Apply the power rule to f(x) = x^2. Here, n = 2, so f'(x) = 2*x^(2-1) = 2*x^1.
  • Step 4: Simplify the derivative. f'(x) = 2x.
  • Step 5: Now, we need to find the derivative at x = 3. Substitute 3 into the derivative: f'(3) = 2*3.
  • Step 6: Calculate the result: 2*3 = 6.
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