To show: The derivative of a one-to-one differentiable functionis
Explanation of Solution
Given information:
The function
Formula used:
Thechain rule for differentiation is if f is a function of gthen
Consider the function
Recall that
Differentiate both sides with respect to x ,
Recall that chain rule for differentiation is if f is a function of gthen
Apply it.
Divide both sides by
Hence, it is proved that thederivative of a one-to-one differentiable function is
To calculate: The value of the expression
Answer to Problem 41E
The value of the expression
Explanation of Solution
Given information:
The values
Formula used:
If
Calculation:
Consider the provided values
Recall that if
So, to evaluate the value of
Since,
Thus, the value of the expression
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