Homework Help is Here – Start Your Trial Now!
Math
Calculus
1 94. Prove that the derivative of f(x) = In x is f'(x) %3D by completing these steps.

1 94. Prove that the derivative of f(x) = In x is f'(x) %3D by completing these steps.

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question

Please do it step by step, please provide the name of the property that you use here. part d is our question to solve, while the second file is just additional info.

Thanks.

94. Prove that the derivative of f(x) = In x is f'(x) %3D %3D by completing these steps. d. Complete the proof by finding the limit of the difference quotient in part (a) as h0. I/int: How is this related to the limit you found in part (c)?]
Transcribed Image Text:94. Prove that the derivative of f(x) = In x is f'(x) %3D %3D by completing these steps. d. Complete the proof by finding the limit of the difference quotient in part (a) as h0. I/int: How is this related to the limit you found in part (c)?]
Additional info a. Show that the difference quotient of f(x) can be expressed as fx + h)-f(x) 1/h = In( 1 + b. Let n so that x = h nh. Show that the difference quotient in part (a) can be rewritten as 1/x In 1 + c. Show that the limit of the expression in part (b) as n x is In e'/x 1 Hint: What is %3D lim (1 +
Transcribed Image Text:Additional info a. Show that the difference quotient of f(x) can be expressed as fx + h)-f(x) 1/h = In( 1 + b. Let n so that x = h nh. Show that the difference quotient in part (a) can be rewritten as 1/x In 1 + c. Show that the limit of the expression in part (b) as n x is In e'/x 1 Hint: What is %3D lim (1 +
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
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
SEE MORE TEXTBOOKS