Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Give precise mathematical definitions or descriptions of each of the concepts that follow. Then illustrate the definition with a graph or algebraic example, if possible.

The differential of a differentiable function u(x).

Short Answer

Expert verified

If u(x) is a differentiable function of x, then differential du is equal todu=u'xdx

Step by step solution

01

Step 1. Given Information

The given statement is the differential of a differentiable function u(x).

02

Step 2. Explanation

If u(x) is a differentiable function of x, then differential du is equal to du=u'(x)dx

For example, consider the integral
localid="1649528992394" cosx2(2x)dx=2xcosx2dxLetu(x)=x2dudx=2xdu=2xdx

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.

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

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free