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What is the derivative of f(x) = x^2 + 2x + 1?

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Question: What is the derivative of f(x) = x^2 + 2x + 1?

Options:

  1. 2x + 2
  2. 2x + 1
  3. x + 2
  4. 2x

Correct Answer: 2x + 2

Solution: 

f\'(x) = 2x + 2.

What is the derivative of f(x) = x^2 + 2x + 1?

Practice Questions

Q1
What is the derivative of f(x) = x^2 + 2x + 1?
  1. 2x + 2
  2. 2x + 1
  3. x + 2
  4. 2x

Questions & Step-by-Step Solutions

What is the derivative of f(x) = x^2 + 2x + 1?
  • Step 1: Identify the function you want to differentiate, which is f(x) = x^2 + 2x + 1.
  • Step 2: Use the power rule for differentiation. The power rule states that if you have x^n, the derivative is n*x^(n-1).
  • Step 3: Differentiate each term in the function separately.
  • Step 4: For the first term x^2, apply the power rule: the derivative is 2*x^(2-1) = 2x.
  • Step 5: For the second term 2x, the derivative is 2 (since the derivative of x is 1).
  • Step 6: For the constant term 1, the derivative is 0 (since the derivative of a constant is always 0).
  • Step 7: Combine the derivatives from each term: 2x + 2 + 0.
  • Step 8: Simplify the result to get the final derivative: f'(x) = 2x + 2.
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