Concept explainers
A table of values for f, g, f′, and g′ is given.
(a) If h(x) = f(g(x)), find h′(1).
(b) If H(x) = g(f(x)), find H′(1).
a)
To find: The value
Answer to Problem 53E
The value
Explanation of Solution
Given:
The function is
Result used: Chain Rule:
If h is differentiable at x and g is differentiable at
Calculation:
Obtain the derivative of
Apply the chain rule as shown in equation (1),
Substitute
Consider the values from given table,
Consider the values from given table
Therefore, the derivative of
(b)
To find: The value
Answer to Problem 53E
The value
Explanation of Solution
Given:
The function is
Calculation:
Obtain the derivative of
Apply the chain rule as shown in equation (1),
Substitute
Consider the values from given table
Consider the values from given table
Therefore, the value
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