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

Express the product and quotient rules in Leibniz/ operator notation.

Short Answer

Expert verified

Productrulef'(x)=ddxg(x))*h(x)+ddxh(x))*g(x)f'(x)=g'(x)h(x)+h'(x)g(x)

Quotient Rule

ddxf(x)=ddxg(x)h(x)ddxf(x)=ddxg(x)*h(x)-ddxh(x)*g(x)(h(x))2

Step by step solution

01

Given Information 

Express the product and quotient rules in Leibniz/ operator notation.

02

Step 2:  Derivative 

Lets consider product of functions

f(x) = g(x)*h(x)

Express the product operator notation

ddxf(x)=ddxg(x)*h(x)f'(x)=ddxg(x))*h(x)+ddxh(x))*g(x)f'(x)=g'(x)h(x)+h'(x)g(x)

03

Derivative 

Lets consider quotient of functions

f(x) = g(x)/h(x)

Express the product operator notation

ddxf(x)=ddxg(x)h(x)ddxf(x)=ddxg(x)*h(x)-ddxh(x)*g(x)(h(x))2f'(x)=g'(x)h(x)-h'(x)g(x)h(x)2

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