Concept explainers
(a)
To sketch: The slope of the function
(a)
Explanation of Solution
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
Graph:
The rough sketch of the derivative function,
(b)
To calculate: The derivative of function
(b)
Answer to Problem 48E
The derivative of
Explanation of Solution
Result used: Chain Rule
If h is differentiable at x and g is differentiable at
Calculation:
Obtain the derivative.
Let
Apply the chain rule as shown in equation (1),
The derivative of
Substitute
Thus, the derivative is
The derivative of
Thus the derivative is
Substitute
Therefore, the derivative of
Graph:
Use the online graphing calculator to draw the graph of the derivative function
From Figure 2, it is observed that the given trigonometric function is differentiable everywhere and the rough sketch of 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