Concept explainers
(a)
To find: The derivative of
(a)
Answer to Problem 47E
The derivative of
Explanation of Solution
Given:
The function is
Result used:
The Power Rule combined with the Chain Rule:
If n is any real number and
Derivative Rule: Product Rule:
If
Calculation:
Obtain the derivative of
Apply the product rule as shown in equation (2),
Apply the power rule combined with the chain rule as shown in equation (1),
Simplify further and obtain the derivative,
Therefore, the derivative of
(b)
To sketch: The graph of
(b)
Explanation of Solution
Given:
The function is
The derivative of
Graph:
Use the online graphing calculator and draw the graph of the functions as shown below in Figure 1.
From Figure 1 it is observe that,
If
If
If
Hence, 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