Explanation Given Information: The provided function is, y = ln ( x 4 + 1 ) 3 Formula used: Property of logarithms: ln ( M p ) = p ln M The differential d d x ( c f ( x ) ) can be written as c ⋅ d d x f ( x ) where c is any non-zero real number. If y = ln u , where u is a differentiable function of x , then d y d x = 1 u ⋅ d u d x For functions f ( x ) and g ( x ) , d d x [ f ( x ) ± g ( x ) ] = d d x f ( x ) ± d d x g ( x ) According to the power rule of derivatives: d d x ( x n ) = n x n − 1 Calculation: Consider the provided function: y = ln ( x 4 + 1 ) 3 First, take the derivative of both sides of the equation with respect to x as: d y d x = d d x [ ln ( x 4 + 1 ) 3 ] Use the property of logarithms ln ( M p ) = p ln M . Then, d y d x = d d x [ ln ( x 4 + 1 ) 3 ] = d d x [ 3 ⋅ ln ( x 4 + 1 ) ] Now, for any non-zero real number c , d d x ( c f ( x ) ) = c ⋅ d d x f ( x ) . d y d x = d d x [ 3 ⋅ ln ( x 4 + 1 ) ] = 3 ⋅ d d x [ ln ( x 4 + 1 ) ] Now, if y = ln u , where u is a differentiable function of x , then d y d x = 1 u ⋅ d u d x

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ISBN: 9780357865095

Author: HARSHBARGER

Publisher: CENGAGE L

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Chapter 11, Problem 3T

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Chapter 11 Solutions

MATHEMATICAL APPLICATIONS FOR THE MGT

Ch. 11.1 - 1. Ch. 11.1 - 2. If Ch. 11.1 - Prob. 3CP Ch. 11.1 - 4. Find . Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Find the derivatives of the functions in Problems...

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The derivative of the function y = ln ( x 4 + 1 ) 3 .

Solution Summary: The author explains how to calculate the derivative of the function y=mathrmln(x4+1)3.

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Chapter 11 Solutions