If f(x) = x , then find the value %3D of f'(a). write solution in excct form.

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...
icon
Related questions
icon
Concept explainers
Question
### Problem Statement

10. If \( f(x) = x^{1/x} \), then find the value of \( f'(2) \). Write the solution in exact form.

### Explanation

This is a mathematical problem involving the differentiation of the function \( f(x) = x^{1/x} \). To find \( f'(2) \), we need to follow these steps:

1. **Rewrite the Function**: Express the given function \( f(x) = x^{1/x} \) in a form that is easier to differentiate.
2. **Differentiate**: Apply the rules of differentiation to find the derivative of the rewritten function.
3. **Evaluate**: Substitute \( x = 2 \) into the derivative to find the exact value of \( f'(2) \).

These steps will guide you through solving the problem correctly.
Transcribed Image Text:### Problem Statement 10. If \( f(x) = x^{1/x} \), then find the value of \( f'(2) \). Write the solution in exact form. ### Explanation This is a mathematical problem involving the differentiation of the function \( f(x) = x^{1/x} \). To find \( f'(2) \), we need to follow these steps: 1. **Rewrite the Function**: Express the given function \( f(x) = x^{1/x} \) in a form that is easier to differentiate. 2. **Differentiate**: Apply the rules of differentiation to find the derivative of the rewritten function. 3. **Evaluate**: Substitute \( x = 2 \) into the derivative to find the exact value of \( f'(2) \). These steps will guide you through solving the problem correctly.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Fundamentals of Algebraic Equations
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning