To calculate: The second derivative of the function
Answer to Problem 31E
The second derivative of the function is
Explanation of Solution
Given information:
The function
Formula used:
The chain rule for differentiation is if f is a function of g then
Power rule for differentiation is
Calculation:
Consider the function
Differentiate both sides with respect to x ,
Recall that power rule for differentiation is
Apply it. Also observe that y is a function of x,
Isolate the value of
Therefore, the value of first derivative of the function is
Now, again differentiate the above expression with respect to x . Recall that quotient rule for differentiation is
Apply it. Also observe that y is a function of x,
Now, substitute the value
According to the question
Thus, the second 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