Concept explainers
Find the derivative o f the function
in two ways: by using the
To find: The derivative of the function
Answer to Problem 2E
The derivative of the function
Explanation of Solution
Given:
The function
Derivative rule:
(1) Quotient Rule: If
(2) Power Rule:
(3). Sum rule:
(4) Constant multiple rule:
(5) Difference rule:
Calculation:
Method 1:
Obtain the derivative of
The derivative of the function
Substitute
Apply the derivative rules (3), (4), and (5),
Apply the power rule (2) and simplify the terms,
Simplify the numerator and obtain the differentiation of
Therefore, the differentiation of the function
Method 2:
Obtain the derivative of
Simplify the function
The derivative of the function
Apply the derivative rules (3), (4) and (5),
Apply the power rule (2) and simplify the terms,
Thus, the differentiation of the function
Therefore, it can be concluded that 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