   Chapter 6.3, Problem 2SWU ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# In Exercises 1-6, find the indicated derivative. f ( x ) = ln ( 2 x + 1 ) ,   f ( 4 ) ( x )

To determine

To calculate: The fourth derivative f4(x) for the function f(x)=ln(2x+1).

Explanation

Given Information:

The function is:

f(x)=ln(2x+1)

Formula used:

The derivative of the polynomial xn is as:

Power rule:

dxndx=nxn1

The derivative of a logarithmic function lnx is:

dlnxdx=1x

Calculation:

Consider the provided function:

f(x)=ln(2x+1)

Now use the formula of the derivative of a logarithmic function lnx is:

dlnxdx=1x

Differentiate the above function with respect to x,

f(x)=1ln(2x+1)×2=2ln(2x+1)

Again, differentiate with respect to x,

f(x)=2(2x+1)2×(1)(2)=4(2x+1)2

Again, differentiate with respect to x

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