   Chapter 11.5, Problem 30E 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.] g ( x ) = ln [ ( 3 x + 1 ) ( − x + 1 ) ] [HINT: See Example 1(b).]

To determine

To calculate: The derivative of the function h(x)=ln[(3x+1)(x+1)].

Explanation

Given information:

The provided function is h(x)=ln[(3x+1)(x+1)].

Formula used:

The derivative of natural logarithm of a function is ddx(lnu)=1ududx, where, u is any function of x

The derivative of the function y=xn by using Power rule is ddx(xn)=nxn1,

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

Calculation:

Consider the provided function h(x)=ln[(3x+1)(x+1)],

Simplify the function h(x)=ln[(3x+1)(x+1)] as,

h(x)=ln[(3x+1)(x+1)]=ln(3x+1)+ln(x+1)

To calculate the derivative of the function h(x)=ln[(3x+1)(x+1)], apply the derivative of natural logarithm of a function that is ddx(lnu)=1ududx

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