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Calculus / Thomas' Calculus: Early Transcendentals 13 / Chapter 3.3 / Problem 47E

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

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Chapter 3, Problem 47E

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QUESTION:

Problem 47E

Derivative Calculations

Find the first and second derivatives of the functions.

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QUESTION:

Problem 47E

Derivative Calculations

Find the first and second derivatives of the functions.

ANSWER:

Solution

Step 1 of 2

In this problem, we have to find the first and second derivatives of the functions.

Given the function is $r=\frac{(\theta{}-1)({\theta{}}^{2}+\theta{}+1)}{{\theta{}}^{3}}$

This function can be rewritten as

$r=\frac{{\theta{}}^{3}+{\theta{}}^{2}+\theta{}-{\theta{}}^{2}-\theta{}-1}{{\theta{}}^{3}}$

$r=\frac{{\theta{}}^{3}-1}{{\theta{}}^{3}}$

$r=1-\frac{1}{{\theta{}}^{3}}$

The first derivative is

$\frac{dr}{d\theta{}}=-(-3\frac{1}{{\theta{}}^{4}})$

$\frac{dr}{d\theta{}}=3\frac{1}{{\theta{}}^{4}}$

This is first derivative of given function

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Solution Found!

Derivative CalculationsFind the first and

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Study Tools You Might Need

Chapter: 1 Problem: 1-3

Chapter: 5 Problem: 82P

Chapter: 4 Problem: 20

Chapter: Problem: 1.30

Chapter: 6 Problem: 6.66

Chapter: 2 Problem: 2-10

Chapter: 4 Problem: 15

Chapter: 9 Problem: 7

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