Concept explainers
To prove: The derivative inverse sine trigonometric functionis
Explanation of Solution
Given information:
The expression
Formula used:
If
Consider the function
Now the derivative of the function is
For the function
Recall that if
Apply it.
Recall the Pythagorean identity,
Consider the positive sign for
Now, substitute the value of
Hence, it is proved that thederivative inverse sine trigonometric function is
To prove: The derivative inverse sine trigonometric function is
Explanation of Solution
Given information:
The expression
Formula used:
If
Consider the function
Now the derivative of the function is
For the function
Recall that if
Apply it.
Recall the Pythagorean identity,
Now, substitute the value of
Hence, it is proved that thederivative inverse sine trigonometric 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