(a)
To find: The derivative of
(a)
Answer to Problem 55E
The derivative of
Explanation of Solution
Given:
The function is
Result used: Chain Rule
If h is differentiable at x and g is differentiable at
The slope of the line passing through the points
Calculation:
Obtain the value of
Apply the chain rule as shown in equation (1),
Substitute
From the given graph, it is observed that
From the given graph, the function
Obtain the values
Since the slope of the line at every point is equal, the slope of the function
Therefore, the value of
The slope of the function
Therefore, the value of
Substitute
Therefore, the value
(b)
To find: The value
(b)
Answer to Problem 55E
The function
Explanation of Solution
Given:
The function is
Calculation:
Obtain the derivative of
Apply the chain rule as shown in equation (1),
Substitute
From the graph observe that,
Obtain the slope of
From the given graph, it is observed that the function
Therefore, it can be concluded that the function
(c)
To find: The value
(c)
Answer to Problem 55E
The value
Explanation of Solution
Given:
The function is
Calculation:
Obtain the derivative of
Apply the chain rule as shown in equation (1),
Substitute
From the graph observe that,
The function
Obtain the value
Since the slope of the line at every point is equal, the slope of the function
Therefore, the value of
Obtain the value
The slope of the function
Therefore, the value of
Substitute
Therefore, the derivative 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