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What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)

Practice Questions

Q1
What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)
  1. 6x^2 - 18x + 12
  2. 6x^2 - 18x
  3. 6x^2 + 18x
  4. 6x^2 - 12

Questions & Step-by-Step Solutions

What is the derivative of f(x) = 2x^3 - 9x^2 + 12x? (2021)
  • Step 1: Identify the function f(x) = 2x^3 - 9x^2 + 12x.
  • 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 2x^3, the derivative is 3 * 2x^(3-1) = 6x^2.
  • Step 5: For the second term -9x^2, the derivative is 2 * -9x^(2-1) = -18x.
  • Step 6: For the third term 12x, the derivative is 1 * 12x^(1-1) = 12.
  • Step 7: Combine all the derivatives from each term: f'(x) = 6x^2 - 18x + 12.
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