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If f(x) = ln(x), what is f'(1)? (2020)

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Question: If f(x) = ln(x), what is f\'(1)? (2020)

Options:

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

Correct Answer: 1

Exam Year: 2020

Solution: 

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

If f(x) = ln(x), what is f'(1)? (2020)

Practice Questions

Q1
If f(x) = ln(x), what is f'(1)? (2020)
  1. 1
  2. 0
  3. undefined
  4. ln(1)

Questions & Step-by-Step Solutions

If f(x) = ln(x), what is f'(1)? (2020)
  • 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 x = 1 into the derivative f'(x). This means we calculate f'(1) = 1/1.
  • Step 4: Simplify the result from Step 3. 1/1 equals 1.
  • Step 5: Conclude that f'(1) = 1.
  • Derivative of Natural Logarithm – Understanding how to differentiate the natural logarithm function and evaluate it at a specific point.
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