   Chapter 11.5, Problem 33E 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.] r ( x ) = ln | ( x + 1 ) ( x − 3 ) − 2 x − 9 |

To determine

To calculate: The derivative of the function r(x)=ln|(x+1)(x3)2x9|.

Explanation

Given information:

The provided function is r(x)=ln|(x+1)(x3)2x9|.

Formula used:

The derivative of natural logarithm of a function is ddx(lnu)=1ududx.

Constant multiple rule of derivative of function f(x) is f(cx)=cf(x) where, c is constant.

The derivative of the function using power rule, y=xn is dydx=nxn1.

Calculation:

Consider the provided function r(x)=ln|(x+1)(x3)2x9|,

Simplify the function r(x)=ln|(x+1)(x3)2x9| as,

r(x)=ln|(x+1)(x3)2x9|=ln[(x+1)(x3)]ln[2x9]=ln(x+1)+ln(x3)ln(2x9)

To calculate the derivative, apply the derivative of natural logarithm of a function is ddx(lnu)=1ududx

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