Short Answer

Use the definition of the derivative to find $f$ for each function $f$ in Exercises 39-54.
$f (x) = \frac{x^{2} - 1}{x^{2} - x - 2}$

The derivative is $f^{'} (x) = \frac{2 x (x^{2} - x - 2) - (2 x - 1) (x^{2} - 1)}{{(x^{2} - x - 2)}^{2}}$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

Given function $f (x) = \frac{x^{2} - 1}{x^{2} - x - 2}$

Step 2: Use the chain rule and calculate

Calculating, we get

$f (x) = \frac{x^{2} - 1}{x^{2} - x - 2} f' (x) = \frac{(x^{2} - x - 2) (2 x) - (x^{2} - 1) (2 x - 1)}{{(x^{2} - x - 2)}^{2}} f' (x) = \frac{2 x (x^{2} - x - 2) - (2 x - 1) (x^{2} - 1)}{{(x^{2} - x - 2)}^{2}}$

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Calculus

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Short Answer

Use the definition of the derivative to find $f$ for each function $f$ in Exercises 39-54.
$f (x) = \frac{x^{2} - 1}{x^{2} - x - 2}$

Step by Step Solution

Step 1: Given information

Step 2: Use the chain rule and calculate

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Calculus

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Use the definition of the derivative to find f for each function f in Exercises 39-54.f(x)=x2-1x2-x-2

Step by Step Solution

Step 1: Given information

Step 2: Use the chain rule and calculate

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Use the definition of the derivative to find $f$ for each function $f$ in Exercises 39-54.
$f (x) = \frac{x^{2} - 1}{x^{2} - x - 2}$