Explanation Given: The given function is f ( x ) = log 5 ( x e x ) Concept Used: 1. Power rule of differentiation d d x x n = n x n − 1 2. log 5 ( x ) = ln ( x ) ln ( 5 ) 3 .Chain rule of differentiation is: d d x f [ g ( x ) ] = d d g f ( g ) d g d x , where g is a differentiable function at x and f is a differentiable function at g ( x ) 4. Product rule of differentiation d d x [ f ( x ) g ( x ) ] = f ( x ) d d x [ g ( x ) ] + g ( x ) d d x [ f ( x ) ] Calculation: To find the derivative of the function f ( x ) = log 5 ( x e x ) First, simplify the right hand side as, log 5 ( x e x ) = ln ( x e x ) ln ( 5 ) Now differentiate both sides of above function with respect to x as, d d x [ f ( x ) ] = d d x [ log 5 ( x e x ) ] = d d x [ ln ( x e x

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 3.7, Problem 6E

To determine

To differentiate the function

f(x)=log5(xex)

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Chapter 3.7, Problem 5E

Chapter 3.7, Problem 7E

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To differentiate the function f ( x ) = log 5 ( x e x )

Solution Summary: The author explains how to find the derivative of the function f(x)=mathrmlog_5.

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To differentiate the function

f(x)=log5(xex)

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Chapter 3 Solutions

To differentiate the function f ( x ) = log 5 ( x e x )

Solution Summary: The author explains how to find the derivative of the function f(x)=mathrmlog_5.

Videos

To differentiate the function f(x)=log5(xex)

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Chapter 3 Solutions

To differentiate the function

f(x)=log5(xex)