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Find the derivative of f(x) = 3x^2 + 5x - 7.

Practice Questions

Q1
Find the derivative of f(x) = 3x^2 + 5x - 7.
  1. 6x + 5
  2. 3x + 5
  3. 6x - 5
  4. 3x^2 + 5

Questions & Step-by-Step Solutions

Find the derivative of f(x) = 3x^2 + 5x - 7.
Correct Answer: 6x + 5
  • Step 1: Identify the function f(x) = 3x^2 + 5x - 7.
  • Step 2: Recognize that we need to find the derivative, which tells us the rate of change of the function.
  • Step 3: Apply the power rule for derivatives: If f(x) = ax^n, then f'(x) = n * ax^(n-1).
  • Step 4: For the first term 3x^2, apply the power rule: The derivative is 2 * 3 * x^(2-1) = 6x.
  • Step 5: For the second term 5x, apply the power rule: The derivative is 1 * 5 * x^(1-1) = 5.
  • Step 6: For the constant term -7, the derivative is 0 because the derivative of any constant is 0.
  • Step 7: Combine the derivatives from Steps 4, 5, and 6: f'(x) = 6x + 5 + 0.
  • Step 8: Simplify the expression: f'(x) = 6x + 5.
  • Power Rule – The power rule states that the derivative of x^n is n*x^(n-1).
  • Constant Rule – The derivative of a constant is zero.
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