To find: The composite function in the form
Answer to Problem 3E
The inner function is
The derivative of y is
Explanation of Solution
Given:
The function is
Formula used:
The Chain Rule:
If h is differentiable at x and g is differentiable at
Power Rule:
If n is positive integer, then
Calculation:
Let the inner function be
Then,
Therefore,
Hence, the inner function is
Thus, the required form of composite function is
Obtain the derivative of y.
Let
Apply the chain rule as shown in equation (1),
The derivative
Substitute
Thus, the derivative
The derivative of
Apply the power rule as shown in equation (2),
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