a.
Explain the proof of the given relation using chain rule.
a.
Explanation of Solution
Given:
The given relationis
Calculation:
From L.H.S
Apply chain rule.
Let
Use derivative rule.
Substitute the value of
Hence
b.
Find the derivative of the given function and sketch the graph of function and its derivative.
b.
Answer to Problem 92E
The derivative of the function is
Explanation of Solution
Given:
The given function is
Calculation:
where
Apply chain rule.
Let
Use derivative rule.
Substitute the value of
The graph of the function and its derivative is given below.
Green line shows the graph of the function and blue line shows the graph of its derivative.
Hence the derivative of the function is
c.
Find the derivative of the given function and sketch the graph of function and its derivative.
c.
Answer to Problem 92E
The derivative of the function is
Explanation of Solution
Given:
The given function is
Calculation:
where
Apply chain rule.
Let
Use derivative rule.
Substitute the value of
The graph of the function and its derivative is given below.
Green line shows the graph of the function and blue line shows the graph of its derivative.
Hence the derivative of the 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