   Chapter 11, Problem 12RE 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 1-32, find the derivative of the given function. f ( x ) = ( | x | + x ) ( 2 − 3 x 2 )

To determine

To calculate: The derivative of the function f(x)=(|x|+x)(23x2).

Explanation

Given Information:

The provided function is f(x)=(|x|+x)(23x2).

Formula used:

Product 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)

Derivative of a constant is 0.

Power rule of a function f(x)=xn is,

f(x)=nxn1

Where, n is some constant.

Constant multiple rule of derivative of function f(x) is ddx[cf(x)]=cddx[f(x)].

Where, c is constant.

Sum and Difference rule of derivative is ddx[f(x)±g(x)]=ddx[f(x)]±ddx[g(x)]

where, f(x) and g(x) are any two differentiable functions.

Derivative of function f(x)=|x| is f(x)=|x|x.

Calculation:

Consider the function,

f(x)=(|x|+x)(23x2)

Apply product rule as,

f'(x)=ddx(|x|+x)(23x2)+(|x|

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