   Chapter 8.4, Problem 3SWU ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# In Exercises 1-4, find the derivative of the function. f ( x )   =   ( x   -   1 ) ( x 2 +   2 x   +   3 )

To determine

To calculate: The derivative of the function f(x)=(x1)(x2+2x+3).

Explanation

Given Information:

The provided function is f(x)=(x1)(x2+2x+3).

Formula used:

General power rule of differentiation:

ddx[xn]=nxn1

Product rule of differentiation:

ddx[a(x)b(x)]=a(x)b(x)+b(x)a(x)

The sum and difference formula of differentiation:

ddx[f(x)+g(x)]=f(x)+g(x)

Calculation:

Consider the provided function is,

f(x)=(x1)(x2+2x+3)

Apply the product rule of differentiation.

f(x)=(x1)ddx[x2+2x+3]+(x2+2x+3)ddx[x1]

Apply the sum and difference formula of differentiation to find the derivative of the above function.

(x1)ddx[x2+2x+3]+(x2+2x+3)ddx[x1]=(x1)(ddx[x2]+ddx[2x]+ddx)+(x2+2x+3)(ddx[x]ddx)

Factor out the real numbers and substitute ddx=0 and ddx=0 in the above function

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