   Chapter 11.4, Problem 38E 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 1-50, calculate the derivate of the function. [HINT: See Example 1.] s ( x ) = ( 3 x − 9 2 x + 4 ) 3

To determine

To calculate: The derivative of the function s(x)=(3x92x+4)3.

Explanation

Given Information:

The provided function is s(x)=(3x92x+4)3.

Formula used:

Quotient rule of derivative of differentiable functions, f(x) and g(x) is,

ddx[f(x)g(x)]=f'(x)g(x)f(x)g'(x)[g(x)]2 where, g(x)0.

A derivative of a function f(x)=(u)n using chain rule is f'(x)=ddx(un)=nun1dudx, where u is the function of x.

Sum and difference rule of the derivative is ddx[f(x)±g(x)]=ddxf(x)±ddxg(x).

Calculation:

Consider the function s(x)=(3x92x+4)3.

Apply chain rule,

s'(x)=3(3x92x+4)31ddx(3x92x+4)=3(3x92x+4)2ddx(3x92x+4)

Apply the quotient rule to the function (3x92x+4),

s'(x)=3(3x92x+4)2[(ddx(3x9))(2x+4)(3

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