(a)
To find: The derivative
(a)
Answer to Problem 47E
The derivative of the equation is
Explanation of Solution
Given:
The equation is
Derivative rules:
Chain rule:
Calculation:
Obtain the derivative the equation by using implicit differentiation.
The equation is
Differentiate implicitly with respect to P,
Apply the product rule and simplify the terms,
Apply the chain rule,
Simplify further and obtain the derivative,
Therefore, the derivative of the equation is
(b)
To find: The rate of change of volume with respect to pressure.
(b)
Answer to Problem 47E
The rate of change of volume with respect to pressure is
Explanation of Solution
Given:
Volume
Pressure
Positive constants
The value
Calculation:
Form part (a), the derivative of the equation is
Substitute
Therefore, the rate of change of volume with respect to pressure is
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning