Concept explainers
To find: The value of
Answer to Problem 35E
The second derivative of the equation at
Explanation of Solution
Given:
The equation
Derivative rules:
(1) Chain rule: If
(2) Product Rule: If
Calculation:
The value of y if
Substitute the value
Take natural logarithmic on both sides,
Thus, the point is
Obtain the second derivative of the equation at
Differentiate implicitly with respect to x,
Apply the product rule (2) and the chain rule (1),
Substitute
Thus, the derivative
Differentiate the equation (1) implicitly with respect to x,
Apply the product rule (2) and the chain rule (1),
Substitute
Therefore, the second derivative of the equation at the point
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