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What is the derivative of f(x) = 1/x?

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Question: What is the derivative of f(x) = 1/x?

Options:

  1. -1/x^2
  2. 1/x^2
  3. -x
  4. x

Correct Answer: -1/x^2

Solution: 

The derivative f\'(x) = d/dx(1/x) = -1/x^2.

What is the derivative of f(x) = 1/x?

Practice Questions

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

Questions & Step-by-Step Solutions

What is the derivative of f(x) = 1/x?
  • Step 1: Start with the function f(x) = 1/x.
  • Step 2: Rewrite 1/x as x^(-1) to make it easier to differentiate.
  • Step 3: Use the power rule for derivatives, which states that d/dx(x^n) = n*x^(n-1).
  • Step 4: Apply the power rule to x^(-1): The derivative is -1 * x^(-1-1) = -1 * x^(-2).
  • Step 5: Rewrite x^(-2) back in fraction form: -1/x^2.
  • Step 6: Conclude that the derivative f'(x) = -1/x^2.
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