   Chapter 11.4, Problem 49E 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 + ( 1 + ( 1 + 2 x ) 3 ) 3 ) 3

To determine

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

Explanation

Given Information:

The provided function is f(x)=(1+(1+(1+2x)3)3)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+(1+(1+2x)3)3)3

Let, (1+(1+2x)3)3=u

So, f(x)=(1+u)3

Apply chain rule,

f(x)=ddx(1+u3)3=3(1+u)2dudx

Substitute u=(1+(1+2x)3)3 and simplify,

f'(x)=3(1+(1+(1+2x)3)3)2ddx((1+(1+2x

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