   Chapter 11.4, Problem 41E 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.] f ( x ) = [ ( 1 + 2 x ) 4 − ( 1 − x ) 2 ] 3

To determine

To calculate: The derivative of the function f(x)=[(1+2x)4(1x)2]3.

Explanation

Given Information:

The provided function is f(x)=[(1+2x)4(1x)2]3.

Formula used:

Derivative of function f(x)=(u)n using chain rule is

f(x)=ddx(u)n=nun1dudx,

Where, u is the function of x.

Calculation:

Consider the function f(x)=[(1+2x)4(1x)2]3,

Let (1+2x)=u,(1x)=v

So, f(x)=[u4v2]3

Apply chain rule,

f(x)=ddxf(x)=[u4v2]3=3[u4v2]2[4u3dudx2vdvd

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