Concept explainers
To calculate: The derivative and the domain of the function
Answer to Problem 23E
The derivative of the function is
Explanation of Solution
Given information:
The function
Formula used:
Thechain rule for differentiation is if f is a function of gthen
Power rule for differentiation is
Product rule for differentiation is
Domain of the function is the set of values of independent variable for which function is defined.
The function of the form
Calculation:
Consider the function
Differentiate both sides with respect to x ,
Recall that quotient rule for differentiation is
Apply it.
Simplify it further as,
Thus, the derivative of the function is
Consider the function,
Recall that domain of the function is the set of values of independent variable for which function is defined.
The function of the form
The provided expression
Also, logarithmic function is defined for positive values, that is,
So, for the function to be defined
Combine the above two inequalities and write in interval notation.
Therefore, domain is
Hence, the domain of the function
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