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 find f'for each function fin Exercises 34-59

f(x)=1x2

Short Answer

Expert verified

The value off'(x)=-2x3

Step by step solution

01

Step 1. Given  information

The given functionf(x)=1x2

02

Step 2. Finding the value of f'(x)

We know that f'(x)=limh0f(x+h)-f(x)h.........(1)

Given f(x)=1x2the

Putting the values in (1)

localid="1648748944158" role="math" f'(x)=limh01(x+h)2-1x2h=limh0x2-(x+h)2x2(x+h)2h=limh0x2-x2-h2-2xhx2(x+h)2h=limh0-h2-2xhx2(x+h)2h=limh0h(-h-2x)x2(x+h)2h=limh0h(-h-2x)x2(x+h)2×1h=limh0(-h-2x)x2(x+h)2

Putting h=0

=-(0)-2xx2.(x+0)2=-2xx2.x2=-2x3

Hence,the value off'(x)=-2x3

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