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%3Dby completing these steps.d. Complete the proof by finding the limit of thedifference quotient in part (a) as h0.I/int: How is this related to the limit youfound in part (c)?] Additional infoa. Show that the difference quotient of f(x) can beexpressed asfx + h)-f(x)1/h= In( 1 +b. Let nso that x =hnh. Show that the differencequotient in part (a) can be rewritten as1/xIn 1 +c. Show that the limit of the expression in part (b)as n x is In e'/x1Hint: What is%3Dlim (1 +

The given function is f(x)=ln x

Answered: 1 94. Prove that the derivative of f(x)…

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Calculus

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

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...

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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)?]

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 +

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