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

Use the definition of the derivative to prove the following special case of the product rule

ddx(x2f(x))=2xf(x)+x2f'(x)

Short Answer

Expert verified

We proved the special case of product function using the definition of the derivative

Step by step solution

01

Given information

We are given a functionddx(x2f(x))=2xf(x)+x2f'(x)

02

Find the derivative

Consider g(x)=x2f(x)

Using the definition of derivative we get,

limh0g(x+h)-g(x)hlimh0(x+h)2f(x+h)-x2f(x)hlimh0(x2+2xh+h2)f(x+h)-x2f(x)hlimh0x2(f(x+h)-f(x))h+limh0h(2x+h)f(x+h)h=x2f'(x)+2xf(x)

Hence proved

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

Most popular questions from this chapter

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free