Concept explainers
To calculate: The derivative of the function
Answer to Problem 31E
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
Derivative of inverse trigonometric function
Calculation:
Consider the function
Differentiate both sides with respect to x ,
Recall that thechain rule for differentiation is if f is a function of gthen
Derivative of inverse trigonometric function
Apply it,
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
Therefore, domain is
Consider the function,
Recall that domain of the function is the set of values of independent variable for which function is defined.
The domain of inverse cosine trigonometric function is
Therefore, domain is
Hence, the derivative of the function is
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