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

Practice Questions

Q1
What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?
  1. 3x^2 - 6x + 4
  2. 3x^2 - 6x
  3. 2x^2 - 3x + 4
  4. 3x^2 + 4

Questions & Step-by-Step Solutions

What is the derivative of f(x) = x^3 - 3x^2 + 4x - 5?
  • Step 1: Identify the function f(x) = x^3 - 3x^2 + 4x - 5.
  • Step 2: Recall the power rule for derivatives: If f(x) = x^n, then f'(x) = n*x^(n-1).
  • Step 3: Apply the power rule to each term in the function.
  • Step 4: For the first term x^3, the derivative is 3*x^(3-1) = 3x^2.
  • Step 5: For the second term -3x^2, the derivative is -3*2*x^(2-1) = -6x.
  • Step 6: For the third term 4x, the derivative is 4*1*x^(1-1) = 4.
  • Step 7: The last term -5 is a constant, and its derivative is 0.
  • Step 8: Combine all the derivatives: f'(x) = 3x^2 - 6x + 4.
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