Concept explainers
To calculate: The derivative of the function
Answer to Problem 35E
The derivative of the function is
Explanation of Solution
Given information:
The function
Formula used:
Thechain rule for
Power rule for differentiation is
Product rule for differentiation is
Derivative of inverse sine function is
Calculation:
Consider the function
Differentiate both sides with respect to x ,
Recall that power rule for differentiation is
Also for the terms of the above expression, apply the product rule for differentiation.
Recall that product rule for differentiation is
Apply it.
Thus, the derivative of the function is
Now, use a graphing window to plot the function and its derivative. Sketch the graph of
The blue curve depicts the graph of
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