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What is the derivative of f(x) = x^3 - 4x + 6?

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Question: What is the derivative of f(x) = x^3 - 4x + 6?

Options:

  1. 3x^2 - 4
  2. 3x^2 + 4
  3. x^2 - 4
  4. 3x^2 - 6

Correct Answer: 3x^2 - 4

Solution: 

The derivative f\'(x) = d/dx(x^3 - 4x + 6) = 3x^2 - 4.

What is the derivative of f(x) = x^3 - 4x + 6?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the derivative of f(x) = x^3 - 4x + 6?
  • Step 1: Identify the function you want to differentiate, which is f(x) = x^3 - 4x + 6.
  • 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 the first term x^3. The derivative is 3*x^(3-1) = 3x^2.
  • Step 4: Apply the power rule to the second term -4x. The derivative is -4*1 = -4.
  • Step 5: The third term is a constant (6). The derivative of a constant is 0.
  • Step 6: Combine all the derivatives from Steps 3, 4, and 5. So, f'(x) = 3x^2 - 4 + 0.
  • Step 7: Simplify the expression. The final derivative is f'(x) = 3x^2 - 4.
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