   Chapter 4.5, Problem 62E ### 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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# Finding Second Derivatives In Exercises 57-62, find the second derivative of the function. f ( x ) = log 9 x

To determine

To calculate: The value of second order derivative of the function f(x)=log9x.

Explanation

Given information:

The provided function is f(x)=log9x.

Formula used:

As with the natural logarithm function if a and x is a positive number such that a1 and x1 then as per change-of-base formula, logax=lnxlna

The derivative of logarithmic function is:

ddx(lnx)=1x

For, x>0

Calculation:

Consider the function,

f(x)=log9x

Apply change-of-base formula to the function:

log9x=lnxln9

The first order derivative of function f(x)=log9x is,

f(x)=ddx(lnxln9)=1ln9ddx(lnx)=1ln9(1x)=1ln<

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