(a)
To show: The derivative of the inverse function
(a)
Explanation of Solution
Given:
The function
Derivative rules:
Chain rule:
Proof:
Obtain the derivative of the function
Since the function
Let
Differentiate implicitly with respect to x.
Apply the chain rule and simplify the terms,
Substitute
Divided by
Hence the required result is proved.
(b)
To find: The value
(b)
Answer to Problem 53E
The value of
Explanation of Solution
Given:
The values
Calculation:
Obtain the value of
From part (a),
Substitute 5 for x,
Since the function is one to one,
Substitute
Therefore, the value of
Chapter 3 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning