Whether the statement, “If f is differentiable, then
Answer to Problem 4RQ
The statement is true.
Explanation of Solution
Result used: Chain Rule
If g is differentiable at t and f is differentiable at
Calculation:
Consider
Take the left hand side
Let
Apply the chain rule as shown in equation (1),
The derivative
Simplify further and obtain the derivative,
Substitute
Thus, the derivative
The derivative of
Thus, the derivative of
Substitute
Thus, the left hand side is equal to the right hand side.
Therefore, the given statement is true.
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