   Chapter 4.5, Problem 14E ### 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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# Differentiating Logarithmic Functions In Exercises 1-22, find the derivative of the function. See Examples 1, 2, 3, and 4. y = ln x x 2 + 1

To determine

To calculate: The derivative of the function y=lnxx2+1.

Explanation

Given information:

The provided function is y=lnxx2+1.

Formula used:

Let a be a positive real number a1 and u be a differentiable function of x. The derivative of natural logarithm of a function is,

ddx[logau]=(1lna)(1u)dudx

As with the natural logarithm function, if x and y are positive numbers such that x1 and y1 then logxy=lnxlny.

Calculation:

Consider the function, y=lnxx2+1

Apply the property of logarithm,

y=lnxln(

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