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

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

Options:

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

Correct Answer: 3x^2 - 4

Solution: 

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

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

Practice Questions

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

Questions & Step-by-Step Solutions

What is the derivative of f(x) = x^3 - 4x?
  • Step 1: Identify the function you want to differentiate. In this case, the function is f(x) = x^3 - 4x.
  • Step 2: Recall the power rule for differentiation. The power rule states that if you have x^n, the derivative is n*x^(n-1).
  • Step 3: Apply the power rule to the first term, x^3. The derivative of x^3 is 3*x^(3-1) = 3x^2.
  • Step 4: Apply the power rule to the second term, -4x. The derivative of -4x is -4 (since the derivative of x is 1).
  • Step 5: Combine the results from Step 3 and Step 4. The derivative f'(x) = 3x^2 - 4.
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