To calculate: The
Answer to Problem 46E
The
Explanation of Solution
Given information:
The function
Formula used:
Thechain rule for
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.
Recall that product rule for differentiation is
Apply it.
Similarly, for the second derivative,apply the product rule for differentiation that is
Similarly, find the third derivative,apply the product rule for differentiation that is
When derivatives are evaluated in same pattern it is observed that all terms except the first term will be a constant number in the eight derivative.
It is known that derivative of a constant term is zero. So, in the ninth derivative, all terms except the first term becomes zero.
Now, eighth derivative of the function is,
And ninth derivative is,
Thus, the
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