Concept explainers
To calculate: The derivative of the function
Answer to Problem 35E
The derivative of the function is
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
Logarithmic rule for differentiation is
Laws of logarithms which are expressed as,
Calculation:
Consider the function
Taking log both sides, we get,
Recall the laws of logarithms which are expressed as,
Apply them,
Differentiate both sides with respect to x ,
Recall that logarithmic rule for differentiation is
Also apply power rule for differentiation in the terms of above expression.
Apply it. Also observe that y is a function of x,
Isolate the value of
Thus, the derivative of the function is
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