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What is the derivative of f(x) = 5x^4?

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Question: What is the derivative of f(x) = 5x^4?

Options:

  1. 20x^3
  2. 5x^3
  3. 15x^3
  4. 4x^3

Correct Answer: 20x^3

Solution: 

The derivative f\'(x) = d/dx(5x^4) = 20x^3.

What is the derivative of f(x) = 5x^4?

Practice Questions

Q1
What is the derivative of f(x) = 5x^4?
  1. 20x^3
  2. 5x^3
  3. 15x^3
  4. 4x^3

Questions & Step-by-Step Solutions

What is the derivative of f(x) = 5x^4?
  • Step 1: Identify the function you want to differentiate. In this case, the function is f(x) = 5x^4.
  • Step 2: Recall the power rule for derivatives. The power rule states that if you have a term in the form of ax^n, the derivative is a * n * x^(n-1).
  • Step 3: Apply the power rule to the term 5x^4. Here, a = 5 and n = 4.
  • Step 4: Multiply the coefficient (5) by the exponent (4). This gives you 5 * 4 = 20.
  • Step 5: Decrease the exponent by 1. The original exponent was 4, so 4 - 1 = 3.
  • Step 6: Combine the results from Step 4 and Step 5. The derivative is 20x^3.
  • Step 7: Write the final answer. The derivative f'(x) = 20x^3.
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