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Determine the derivative of f(x) = 1/x.

Practice Questions

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

Questions & Step-by-Step Solutions

Determine the derivative of f(x) = 1/x.
Correct Answer: -1/x^2
  • Step 1: Rewrite the function f(x) = 1/x in a different form. This can be done by expressing it as f(x) = x^(-1).
  • Step 2: Identify the power rule for derivatives. The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1).
  • Step 3: Apply the power rule to f(x) = x^(-1). Here, n = -1.
  • Step 4: Calculate the derivative using the power rule: f'(x) = -1 * x^(-1 - 1) = -1 * x^(-2).
  • Step 5: Rewrite the result in a simpler form: f'(x) = -1/x^2.
  • Power Rule – The power rule states that the derivative of x^n is n*x^(n-1). In this case, f(x) = x^(-1).
  • Negative Exponents – Understanding how to handle negative exponents is crucial, as f(x) = 1/x can be rewritten as x^(-1).
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