   Chapter 3.2, Problem 8E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Differentiate. G ( x ) = x 2 − 2 2 x + 1

To determine

To find: The differentiation of the function G(x)=x222x+1.

Explanation

Given:

The function G(x)=x222x+1.

Derivative rule:

(1) Quotient Rule: If f1(x) and f2(x) are both differentiable, then

ddx[f1(x)f2(x)]=f2(x)ddx[f1(x)]f1(x)ddx[f2(x)][f2(x)]2

(2) Power Rule: ddx(xn)=nxn1

(3) Sum rule: ddx(f+g)=ddx(f)+ddx(g)

(4) Constant multiple rule: ddx(cf)=cddx(f)

(5) Difference rule: ddx(fg)=ddx(f)ddx(g)

Calculation:

The derivative of the function is G(x), which is obtained as follows.

g(x)=ddx(G(x))=ddx(x222x+1)

Substitute x22 for f1(x) and 2x+1 for f2(x) in the quotient rule (1),

g(x)=(2x+1)ddx[x22](x22)ddx[2x

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