Explanation Formula used: 1. d ( tan − 1 u ) d x = 1 1 + u 2 ⋅ d u d x 2. d ( u ⋅ v ) d x = v d u d x + u d v d x 3. d ( u v ) d x = v d u d x − u d v d x v 2 . Calculation: The given function is y = x tan − 1 x . Find the first derivative of y = x tan − 1 x as follows. d y d x = d d x ( x tan − 1 x ) = tan − 1 x d d x ( x ) + x d d x ( tan − 1 x ) = tan − 1 x ⋅ ( 1 ) + x ⋅ 1 1 + x 2 = tan − 1 x + x 1 + x 2 Again differentiate d y d x = tan − 1 x + x 1 + x 2 to find the second derivative. d 2 y d x 2 = d d x ( tan − 1 x + x 1 + x 2 ) = d d x ( tan − 1 x ) + d d x ( x 1 + x 2 ) = 1 1 + x 2 +

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ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Question

Chapter 27.3, Problem 41E

To determine

The second derivative of y=xtan−1x.

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Chapter 27.3, Problem 40E

Chapter 27.3, Problem 42E

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Chapter 27 Solutions

Basic Technical Mathematics

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Prob. 7E Ch. 27.7 - Prob. 8E Ch. 27.7 - Prob. 9E Ch. 27.7 - Prob. 10E Ch. 27.7 - Prob. 11E Ch. 27.7 - Prob. 12E Ch. 27.7 - Prob. 13E Ch. 27.7 - Prob. 14E Ch. 27.7 - Prob. 15E Ch. 27.7 - Prob. 16E Ch. 27.7 - Prob. 17E Ch. 27.7 - Prob. 18E Ch. 27.7 - Prob. 19E Ch. 27.7 - Prob. 20E Ch. 27.7 - Prob. 21E Ch. 27.7 - Prob. 22E Ch. 27.7 - Prob. 23E Ch. 27.7 - Prob. 24E Ch. 27.7 - Prob. 25E Ch. 27.7 - Prob. 26E Ch. 27.7 - Prob. 27E Ch. 27.7 - Prob. 28E Ch. 27.7 - Prob. 29E Ch. 27.7 - In Exercises 3–36, evaluate each limit (if it...Ch. 27.7 - Prob. 31E Ch. 27.7 - Prob. 32E Ch. 27.7 - Prob. 33E Ch. 27.7 - Prob. 34E Ch. 27.7 - Prob. 35E Ch. 27.7 - Prob. 36E Ch. 27.7 - Prob. 37E Ch. 27.7 - Prob. 38E Ch. 27.7 - Prob. 39E Ch. 27.7 - Prob. 40E Ch. 27.7 - Prob. 41E Ch. 27.7 - Prob. 42E Ch. 27.7 - Prob. 43E Ch. 27.7 - Prob. 44E Ch. 27.7 - Prob. 45E Ch. 27.7 - Prob. 46E Ch. 27.7 - Prob. 47E Ch. 27.7 - Prob. 48E Ch. 27.8 - Prob. 1PE Ch. 27.8 - In Exercises 1 and 2, make the given changes in...Ch. 27.8 - Prob. 2E Ch. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 4E Ch. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 6E Ch. 27.8 - Prob. 7E Ch. 27.8 - Prob. 8E Ch. 27.8 - Prob. 9E Ch. 27.8 - Prob. 10E Ch. 27.8 - Prob. 11E Ch. 27.8 - In Exercises 3–14, sketch the graphs of the given...Ch. 27.8 - Prob. 13E Ch. 27.8 - Prob. 14E Ch. 27.8 - Prob. 15E Ch. 27.8 - Prob. 16E Ch. 27.8 - Prob. 17E Ch. 27.8 - Prob. 18E Ch. 27.8 - Prob. 19E Ch. 27.8 - Prob. 20E Ch. 27.8 - Prob. 21E Ch. 27.8 - Prob. 22E Ch. 27.8 - Prob. 23E Ch. 27.8 - Prob. 25E Ch. 27.8 - Prob. 26E Ch. 27.8 - Prob. 27E Ch. 27.8 - Prob. 28E Ch. 27.8 - Prob. 29E Ch. 27.8 - Prob. 30E Ch. 27.8 - Prob. 31E Ch. 27.8 - Prob. 32E Ch. 27.8 - Prob. 33E Ch. 27.8 - Prob. 34E Ch. 27.8 - The energy E (in J) dissipated by a certain...Ch. 27.8 - Prob. 36E Ch. 27.8 - Prob. 37E Ch. 27.8 - Prob. 39E Ch. 27.8 - A package of weather instruments is propelled into...Ch. 27.8 - Prob. 41E Ch. 27.8 - Prob. 42E Ch. 27.8 - Prob. 43E Ch. 27.8 - 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The second derivative of y = x tan − 1 x .

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The second derivative of y=xtan−1x.

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Chapter 27 Solutions