Let f(x)=In|x| . After substituting f(x) into the definition of the derivative, which of the following gives the correct representation of f'(x) ? O lim In|x+h|+In]x| h h-0 O lim In|x+h| h h-0 lim Inlx+h|-In|h[| h-0 lim h-0 In|x+h|-In\x|| h lim hln|x+h|+In]x|| h-0 h

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Let f(x)=In|x| . After substituting f(x) into the definition of the derivative, which of the following gives the correct
representation of f'(x) ?
lim In|x+h|+In|x||
h-0
h
In|x+h|
lim
h-0
In|x+h|-In|h|
O lim
h-0
lim
h-0
In|x+h|-In|x||
h
hln|x+h|+In]x|
lim
h-0
h
h
lim
h-0 x+h
lim
h-0 |x+h|
lim hln|x+h|-In]x|
h
h-0
Transcribed Image Text:Let f(x)=In|x| . After substituting f(x) into the definition of the derivative, which of the following gives the correct representation of f'(x) ? lim In|x+h|+In|x|| h-0 h In|x+h| lim h-0 In|x+h|-In|h| O lim h-0 lim h-0 In|x+h|-In|x|| h hln|x+h|+In]x| lim h-0 h h lim h-0 x+h lim h-0 |x+h| lim hln|x+h|-In]x| h h-0
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