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What is the derivative of f(x) = 3x^3 - 5x + 2?

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Question: What is the derivative of f(x) = 3x^3 - 5x + 2?

Options:

  1. 9x^2 - 5
  2. 3x^2 - 5
  3. 9x^2 + 5
  4. 3x^2 + 5

Correct Answer: 9x^2 - 5

Solution: 

f\'(x) = 9x^2 - 5.

What is the derivative of f(x) = 3x^3 - 5x + 2?

Practice Questions

Q1
What is the derivative of f(x) = 3x^3 - 5x + 2?
  1. 9x^2 - 5
  2. 3x^2 - 5
  3. 9x^2 + 5
  4. 3x^2 + 5

Questions & Step-by-Step Solutions

What is the derivative of f(x) = 3x^3 - 5x + 2?
  • Step 1: Identify the function f(x) = 3x^3 - 5x + 2.
  • Step 2: Use the power rule for derivatives, which states that if f(x) = ax^n, then f'(x) = n * ax^(n-1).
  • Step 3: Apply the power rule to each term in the function.
  • Step 4: For the first term 3x^3, the derivative is 3 * 3x^(3-1) = 9x^2.
  • Step 5: For the second term -5x, the derivative is -5 * 1x^(1-1) = -5.
  • Step 6: The constant term 2 has a derivative of 0, since the derivative of any constant is 0.
  • Step 7: Combine the derivatives from each term: f'(x) = 9x^2 - 5 + 0.
  • Step 8: Simplify the expression to get f'(x) = 9x^2 - 5.
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