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

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

Options:

  1. 10x - 4
  2. 10x + 4
  3. 5x - 4
  4. 5x + 4

Correct Answer: 10x - 4

Solution: 

Using the power rule, f\'(x) = 10x - 4.

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

Practice Questions

Q1
What is the derivative of f(x) = 5x^2 - 4x + 3?
  1. 10x - 4
  2. 10x + 4
  3. 5x - 4
  4. 5x + 4

Questions & Step-by-Step Solutions

What is the derivative of f(x) = 5x^2 - 4x + 3?
  • Step 1: Identify the function f(x) = 5x^2 - 4x + 3.
  • Step 2: Recognize that we need to find the derivative, which tells us the rate of change of the function.
  • Step 3: Use the power rule for derivatives, which states that if f(x) = ax^n, then f'(x) = n * ax^(n-1).
  • Step 4: Apply the power rule to the first term 5x^2: The derivative is 2 * 5 * x^(2-1) = 10x.
  • Step 5: Apply the power rule to the second term -4x: The derivative is 1 * -4 * x^(1-1) = -4.
  • Step 6: The third term, 3, is a constant, and its derivative is 0.
  • Step 7: Combine the derivatives from steps 4, 5, and 6: f'(x) = 10x - 4 + 0.
  • Step 8: Simplify the expression: f'(x) = 10x - 4.
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