To find: The derivative
Answer to Problem 62E
The derivative
Explanation of Solution
Given:
The function is
Result used: Chain Rule
If h is differentiable at x and g is differentiable at
Derivative Rules:
Product Rule:
Sum Rule:
Calculation:
Obtain the first derivative of
Apply the product rule (1),
Obtain the derivative
Let
The derivative of
Substitute
Thus, the derivative is
The derivative of
Thus, the derivative is
Substitute
Substitute
Therefore, the derivative of
Obtain the second derivative of
Apply the sum rule (2),
Obtain the derivative
Obtain the derivative
Let
The derivative of
Substitute
Thus the derivative is
The derivative of
Thus the derivative is
Substitute
Substitute
Substitute
Therefore, the derivative
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