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f(x)=(1)/(x-1)

f(x)=1x−1f(x)=\frac{1}{x-1}

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Add, subtract, multiply, or divide two integersright chevron icon

Full solution

Q. f(x)=1x−1f(x)=\frac{1}{x-1}
  1. Question Prompt: Question Prompt: Determine the derivative of the function f(x)=1x−1f(x) = \frac{1}{x-1}.
  2. Calculate Derivative: Calculate the derivative using the power rule: f′(x)=−1×(x−1)−2×(1)f'(x) = -1 \times (x-1)^{-2} \times (1).
  3. Check at Specific Points: Check the derivative at specific points to ensure it behaves as expected. For example, at x=2x = 2, f′(2)=−1(2−1)2=−1f'(2) = -\frac{1}{(2-1)^2} = -1.

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