(a)
To find: The derivative of
(a)
Answer to Problem 26E
The first derivative of
The second derivative of
Explanation of Solution
Given:
The function is
Derivative rules:
(1) Product Rule:
(2)
Calculation:
Obtain the derivative
Apply the product rule (1) and simplify further,
Therefore, the first derivative of
Obtain the second derivative of
Apply the difference rule (2),
Apply the product rule (1),
Therefore, the derivative of
(b)
To check: The derivatives
(b)
Answer to Problem 26E
The derivatives are reasonable.
Explanation of Solution
From part (a), the derivatives of
Graph:
Use the online graphing calculator to draw the graph of the functions as shown below in Figure 1.
Form Figure 1, it is observed that the function
The value of the derivative of the function at any point x can be estimated by drawing the tangent line at any point
Mark the slope of the tangent as a point in y-axis and the value of x as a point in x-axis in the graph of
Proceed in the similar way at several points and obtain the rough graph of the
Hence, it can be concluded that the derivative of the function
The value of the derivative of the function at any point x can be estimated by drawing the tangent line at any point
Mark the slope of the tangent as a point in y-axis and the value of x as a point in x-axis in the graph of
Proceed in the similar way at several points and obtain the rough graph of the
Hence, it can be concluded that the derivative of the function
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