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If f(x) = ln(x), what is f'(e)?

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Question: If f(x) = ln(x), what is f\'(e)?

Options:

  1. 1
  2. 0
  3. e
  4. ln(e)

Correct Answer: 1

Solution: 

f\'(x) = 1/x. Therefore, f\'(e) = 1/e.

If f(x) = ln(x), what is f'(e)?

Practice Questions

Q1
If f(x) = ln(x), what is f'(e)?
  1. 1
  2. 0
  3. e
  4. ln(e)

Questions & Step-by-Step Solutions

If f(x) = ln(x), what is f'(e)?
  • Step 1: Identify the function given in the question, which is f(x) = ln(x).
  • Step 2: Find the derivative of the function f(x). The derivative of ln(x) is f'(x) = 1/x.
  • Step 3: Substitute e into the derivative. We need to find f'(e).
  • Step 4: Calculate f'(e) by replacing x with e in the derivative: f'(e) = 1/e.
  • Derivative of Natural Logarithm – Understanding how to differentiate the natural logarithm function and evaluate it at a specific point.
  • Evaluation of Derivatives – Applying the derivative formula to find the slope of the function at a given value.
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