Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
Please7 show work
![Differentiate.
\[ F(x) = \frac{e^{3x}}{x^9} \]
\[ F'(x) = \_\_\_\_\_ \]
Explanation:
The problem is asking for the derivative of the function \( F(x) \). The function is given as a quotient of \( e^{3x} \) and \( x^9 \). To find \( F'(x) \), the derivative, you would typically apply the quotient rule, which is:
If \( u(x) \) and \( v(x) \) are differentiable functions, then the derivative of the quotient \( \frac{u(x)}{v(x)} \) is:
\[ \left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2} \]
Here, \( u(x) = e^{3x} \) and \( v(x) = x^9 \). You will need to find \( u'(x) \) and \( v'(x) \) and apply the quotient rule accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2539764-cbb6-4f84-96a1-bc799fc276f3%2Fc606835b-c077-44ec-ab4b-78d33706f8a1%2F1mxd3qn_processed.png&w=3840&q=75)
Transcribed Image Text:Differentiate.
\[ F(x) = \frac{e^{3x}}{x^9} \]
\[ F'(x) = \_\_\_\_\_ \]
Explanation:
The problem is asking for the derivative of the function \( F(x) \). The function is given as a quotient of \( e^{3x} \) and \( x^9 \). To find \( F'(x) \), the derivative, you would typically apply the quotient rule, which is:
If \( u(x) \) and \( v(x) \) are differentiable functions, then the derivative of the quotient \( \frac{u(x)}{v(x)} \) is:
\[ \left(\frac{u}{v}\right)' = \frac{u'v - uv'}{v^2} \]
Here, \( u(x) = e^{3x} \) and \( v(x) = x^9 \). You will need to find \( u'(x) \) and \( v'(x) \) and apply the quotient rule accordingly.
Expert Solution
Step 1: Description for the given problem
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning