Chapter 2: Q. 54 (page 184)

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

Short Answer

Expert verified

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

Step by step solution

Given information

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

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

Short Answer

Step by step solution

Given information

Use the chain rule and calculate

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

Short Answer

Step by step solution

Given information

Use the chain rule and calculate

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

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Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

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