   Chapter 3.10, Problem 18E ### 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

# (a) Find the differential dy and (b) evaluate dy for the given values of x and dx.18. y = x + 1 x − 1 ,   x = 2 ,   d x = 0.05

(a)

To determine

To find: The differential dy.

Explanation

Given:

The function is y=x+1x1 and the value x=2 and dx=0.05.

Derivative rules:

(1) Chain rule: If y=f(u) and u=g(x)  are both differentiable function, then

dydx=dydududx.

(2) 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)].

Result used:

The differential is dy=f(x)dx.

Calculation:

The differential of the function is computed as follows,

Consider y=f(x).

f(x)=x+1x1

Differentiate with respect to x,

f(x)=ddx(x+1x1)

Apply Quotient rule and simplify the terms,

f(x)=(x1)ddx(x+1)(x+1)ddx(x1)(x1)2=(x1)[ddx(x+1)](x+1)[ddx(x1)](x1)

(b)

To determine

To evaluate: The value dy for x=2 and dx=0.05.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Problems 39 – 44, solve each inequality and graph the solution. 41.

Mathematical Applications for the Management, Life, and Social Sciences

#### Evaluate the integral, if it exists. x+2x2+4xdx

Single Variable Calculus: Early Transcendentals

#### sec1(23)= a) 3 b) 3 c) 6 d) 6

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 