Chapter 5: Q. 12 (page 417)

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
$u (x) = \frac{1}{x}$

Short Answer

Expert verified

The differential du in terms of the differential dx is $d u = - \frac{1}{x^{2}} d x$ .

Step by step solution

Step 1. Given Information

For given function u(x) we have to write the differential du in terms of the differential dx.

$u (x) = \frac{1}{x}$

Step 2. Now finding the differential du in terms of the differential dx.

$u (x) = \frac{1}{x} u (x) = x^{- 1} \frac{d u}{d x} = - 1 x^{- 2} \frac{d u}{d x} = - \frac{1}{x^{2}} d u = - \frac{1}{x^{2}} d x$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
$u (x) = \frac{1}{x}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Now finding the differential du in terms of the differential dx.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.u(x)=1x

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Now finding the differential du in terms of the differential dx.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Probability and Statistics

Mechanics Maths

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.
$u (x) = \frac{1}{x}$