To calculate: The derivative of the function
Answer to Problem 29E
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
Product rule for differentiation is
Differentiation rule for inverse trigonometric functions is
Calculation:
Consider the function
Let us assume
Differentiate the given function both sides with respect to
Differentiate
Recall that differentiation rule for inverse trigonometric functions is
Simplify it further as,
Recall that
Thus, 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