Explanation Definition used: The derivative of the logarithmic functions of the form ln u is given by the formula d ( ln u ) d x = 1 u d u d x . Calculation: The given equation is V = k ln a 2 + x 2 + a a 2 + x 2 − a where E = − d V d x . Rewrite the given equation as, V = k ln a 2 + x 2 + a a 2 + x 2 − a V = k [ ln ( a 2 + x 2 + a ) − ln ( a 2 + x 2 − a ) ] ( ∵ ln ( u v ) = ln u − ln v ) Using the above definition, differentiate both sides of the above equation and obtain the first derivative as shown below: V = k [ ln ( a 2 + x 2 + a ) − ln ( a 2 + x 2 − a ) ] d V d x = k x a 2 + x 2 ( a 2 + x 2 + a ) − k x a 2 + x 2 ( a 2 + x 2 − a ) d V d x = k x [ a 2 + x 2 − a a 2 + x 2 − ( a 2 + x 2 + a a 2 + x 2 ) ] ( a 2 + x 2 ) ( a 2 + x 2 + a 2 ) d V

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Differential Equations

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Chapter 27.5, Problem 56E

To determine

The expression for the variable E from the equation V=klna2+x2+aa2+x2−a.

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Chapter 27.5, Problem 55E

Chapter 27.6, Problem 1PE

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Chapter 27 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

Ch. 27.1 - Prob. 1PE Ch. 27.1 - Prob. 2PE Ch. 27.1 - Prob. 1E Ch. 27.1 - Prob. 2E Ch. 27.1 - Prob. 3E Ch. 27.1 - Prob. 4E Ch. 27.1 - Prob. 5E Ch. 27.1 - Prob. 6E Ch. 27.1 - Prob. 7E Ch. 27.1 - Prob. 8E

Ch. 27.1 - Prob. 9E Ch. 27.1 - Prob. 10E Ch. 27.1 - Prob. 11E Ch. 27.1 - Prob. 12E Ch. 27.1 - Prob. 13E Ch. 27.1 - Prob. 14E Ch. 27.1 - Prob. 15E Ch. 27.1 - Prob. 16E Ch. 27.1 - Prob. 17E Ch. 27.1 - Prob. 18E Ch. 27.1 - Prob. 19E Ch. 27.1 - Prob. 20E Ch. 27.1 - Prob. 21E Ch. 27.1 - Prob. 22E Ch. 27.1 - Prob. 23E Ch. 27.1 - Prob. 24E Ch. 27.1 - Prob. 25E Ch. 27.1 - In Exercises 3–34, find the derivatives of the...Ch. 27.1 - Prob. 27E Ch. 27.1 - Prob. 28E Ch. 27.1 - Prob. 29E Ch. 27.1 - Prob. 30E Ch. 27.1 - Prob. 31E Ch. 27.1 - Prob. 32E Ch. 27.1 - Prob. 33E Ch. 27.1 - Prob. 34E Ch. 27.1 - Prob. 35E Ch. 27.1 - Prob. 36E Ch. 27.1 - Prob. 37E Ch. 27.1 - Prob. 38E Ch. 27.1 - Prob. 39E Ch. 27.1 - Prob. 40E Ch. 27.1 - Prob. 41E Ch. 27.1 - Prob. 42E Ch. 27.1 - Prob. 43E Ch. 27.1 - Prob. 44E Ch. 27.1 - Prob. 45E Ch. 27.1 - Prob. 46E Ch. 27.1 - Prob. 47E Ch. 27.1 - Prob. 48E Ch. 27.1 - Prob. 49E Ch. 27.1 - Prob. 50E Ch. 27.1 - Prob. 51E Ch. 27.1 - Prob. 52E Ch. 27.1 - Prob. 53E Ch. 27.1 - Prob. 54E Ch. 27.1 - 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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 expression for the variable E from the equation V = k ln a 2 + x 2 + a a 2 + x 2 − a .

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The expression for the variable E from the equation V=klna2+x2+aa2+x2−a.

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Chapter 27 Solutions