To calculate: The value of the function
Answer to Problem 33E
The value of the function
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
Derivative of the inverse sine function is
Product rule for differentiation is
Calculation:
Consider the function
Differentiate both sides with respect to x ,
Recall that power rule for differentiation is
Apply it. Also observe that y is a function of x,
Now, substitute
Recall that the inverse sine trigonometric function is expressed as
Recall that value of sine function at an angle
That is,
Take sine function to the right hand side,
Thus, the value 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