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

Write down a rule for differentiating a composition f(u(v(w(x))))of four functions

(a) in “prime” notation and

(b) in Leibniz notation.

Short Answer

Expert verified

(a) in “prime” notation the derivative is:(fuvw)'(x)=f'(uvw)(x)×u'(vw)(x)×v'(w(x))×w'(x)

(b) in Leibniz notation the derivative is:dfdx=dfdu×dudv×dvdw×dwdx

Step by step solution

01

Step 1. Given information:

The composite function is;

f(u(v(w(x))))

02

Part (a). Step 1. Derivative in prime notation:

The derivative of the given function in prime notation is;(fuvw)'(x)=f'(uvw)(x)×u'(vw)(x)×v'(w(x))×w'(x)

03

Part (b). Step 1. Derivative in Leibniz notation:

In Leibniz notation the derivative of the function is:

dfdx=dfdu×dudv×dvdw×dwdx

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