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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Differentiating Logarithmic Functions In Exercises 1–22, find the derivative of the function. See Examples 1, 2, 3, and 4.

y = ln [ x ( 2 x + 3 ) 2 ]

To determine

To calculate: The derivative of the function y=ln[x(2x+3)2].

Explanation

Given information:

The provided function is y=ln[x(2x+3)2].

Formula used:

The derivative of logarithm function is,

ddxlnu=1ududx

Where u>0

Calculation:

Consider the function is y=ln[x(2x+3)2].

Apply the property of logarithm,

y=lnx+ln(2x+3)2=lnx+2ln(2x+3)

Now, the derivative of given function is,

y=1x

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