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The function f(x) = ln(x) is differentiable at x = 1?

Practice Questions

Q1
The function f(x) = ln(x) is differentiable at x = 1?
  1. Yes
  2. No
  3. Only for x > 1
  4. Only for x < 1

Questions & Step-by-Step Solutions

The function f(x) = ln(x) is differentiable at x = 1?
  • Step 1: Identify the function we are working with, which is f(x) = ln(x).
  • Step 2: Understand that we need to find the derivative of the function to check if it is differentiable at x = 1.
  • Step 3: Use the derivative formula for the natural logarithm, which is f'(x) = 1/x.
  • Step 4: Substitute x = 1 into the derivative formula: f'(1) = 1/1.
  • Step 5: Calculate the result: f'(1) = 1.
  • Step 6: Since the derivative exists and is equal to 1 at x = 1, we conclude that the function f(x) = ln(x) is differentiable at x = 1.
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