   Chapter 3.2, Problem 19E ### 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. y = s − s s 2

To determine

To find: The differentiation of the function y=sss2.

Explanation

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

Calculation:

The derivative of the function y=sss2 is dyds, which is obtained as follows,

dyds=dds(sss2)=dds(ss12s2)

Use the quotient rule (1) and simplify the terms,

dyds=(s2)dds(ss12)(ss12)dds(s2)(s2)2

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