How to Differentiate f(x) = 1 / (x^2 - 4) Using the Limit Definition

Math Problem Statement

Differentiate the function f(x) = 1 / (x^2 - 4) using the limit definition of the derivative.

The image shows a mathematical problem involving the derivative of a function. Here's what I see:

The given function is $f(x) = \frac{1}{x^2 - 4}$ .
The derivative $f'(x)$ is expressed using the limit definition: $f'(x) = \lim_{h \to 0} \frac{\frac{1}{(x+h)^2 - 4} - \frac{1}{x^2 - 4}}{h}.$

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Calculus
Limits
Derivatives

Definition of a derivative: f'(x) = lim (h → 0) [(f(x+h) - f(x)) / h]

Limit Definition of Derivatives

Grades 11-12 or Introductory College Level

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