Explanation Given : The function is y = ( x 2 + 1 ) 4 ( 2 x + 1 ) 3 ( 3 x − 1 ) 5 . Calculation: Take logarithm on both sides of the equation y = ( x 2 + 1 ) 4 ( 2 x + 1 ) 3 ( 3 x − 1 ) 5 as follows: ln y = ln ( ( x 2 + 1 ) 4 ( 2 x + 1 ) 3 ( 3 x − 1 ) 5 ) ln y = ln ( x 2 + 1 ) 4 − ln ( 2 x + 1 ) 3 − ln ( 3 x − 1 ) 5 ln y = 4 ln ( x 2 + 1 ) − 3 ln ( 2 x + 1 ) − 5 ln ( 3 x − 1 ) Differentiate both sides of the equation as follows: d ( ln y ) d x = 4 ( 1 x 2 + 1 ⋅ 2 x ) − 3 ( 1 2 x + 1 ⋅ 2 ) − 5 ( 1 3 x − 1 ⋅ 3 )

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3, Problem 40E

To determine

The derivative of the function y=( x 2 +1)4( 2x+1)3( 3x−1)5 .

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Chapter 3, Problem 39E

Chapter 3, Problem 41E

Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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The derivative of the function y = ( x 2 + 1 ) 4 ( 2 x + 1 ) 3 ( 3 x − 1 ) 5 .

Solution Summary: The author calculates the derivative of the function y=(x2+1)4 (2x+1

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The derivative of the function y=( x 2 +1)4( 2x+1)3( 3x−1)5 .

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Chapter 3 Solutions