Concept explainers
To calculate: The derivative
Answer to Problem 21E
The derivative
Explanation of Solution
Given information:
The function
Formula used:
Thechain rule for differentiation is if f is a function of gthen
Power rule for differentiation is
Product rule for differentiation is
Calculation:
Consider the function
Differentiate both sides with respect to x ,
Recall that power rule for differentiation is
Also for the terms of the above expression, apply the product rule for differentiation.
Apply it,
To find double derivative, again differentiate the function with respect to x ,
Recall the chain rule for differentiation is if f is a function of gthen
Also for the terms of the above expression, apply the product rule for differentiation.
Apply it,
Thus, 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