   Chapter 11.5, Problem 40E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 1-66, find the derivative of the function. [HINT: See Quick Example 5-14.] f ( x ) = 1 ln | x |

To determine

To calculate: The derivative of the function f(x)=1ln|x|.

Explanation

Given information:

The provided function is f(x)=1ln|x|.

Formula used:

Chain rule:

The derivative of function f(x)=un is:

f(x)=ddx(un)=nun1dudx

Where u is the function of x.

The derivative of natural logarithm of x:

ddxln|x|=1x

Calculation:

Consider the function, f(x)=1ln|x|.

Rewrite the function as,

f(x)=1ln|x|=(ln|x|)1

Assume, ln|x|=u.

Then the derivative is,

f(x)=ddxu1

Apply the chain rule to the function u1,

f(x)=1uȡ

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