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
How to show the check point 4please
![EXAMPLE 4
Rewriting Before Differentiating
Find the derivative of
f(x) = In[x(x? + 1)*].
SOLUTION
4.
ion
re
4.
f(x) = In[x(x2 + 1)]
= In x + In(x + 1)2
= In x + 2 In(x + 1)
Write original function.
%3D
Property of logarithms
%3D
Property of logarithms
1
2x
f'(x)
+ 2
%3D
Differentiate,
1
4x
x? + 1
Simplify.
Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.com
Find the derivative of f(x) = Inx /x? + 1
Finding the derivative of the function in Example 4 without first rewriting would
be a formidable task.
1
d.
f(x) =
x(x? + 1)2 drx(xx² + 1)²]
You might try showing that this yields the same result obtained in Example 4, but be
careful-the algebra is messy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb66ed3a-bb57-44f2-a452-789342f659dc%2F3c96fe76-a5df-421b-ab7a-5cbf0afb8657%2F3gl50x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXAMPLE 4
Rewriting Before Differentiating
Find the derivative of
f(x) = In[x(x? + 1)*].
SOLUTION
4.
ion
re
4.
f(x) = In[x(x2 + 1)]
= In x + In(x + 1)2
= In x + 2 In(x + 1)
Write original function.
%3D
Property of logarithms
%3D
Property of logarithms
1
2x
f'(x)
+ 2
%3D
Differentiate,
1
4x
x? + 1
Simplify.
Checkpoint 4 Worked-out solution available at LarsonAppliedCalculus.com
Find the derivative of f(x) = Inx /x? + 1
Finding the derivative of the function in Example 4 without first rewriting would
be a formidable task.
1
d.
f(x) =
x(x? + 1)2 drx(xx² + 1)²]
You might try showing that this yields the same result obtained in Example 4, but be
careful-the algebra is messy.
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