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 differentiation rules developed in this section to find the derivatives of the functions in Exercises 35-64. Note that it may be necessary to do some preliminary algebra before differentiating.

f(x)=(x-x3)2

Short Answer

Expert verified

The derivative of the function isf'(x)=1-53x-16+23x-13.

Step by step solution

01

Step 1. Given Information

The given function isf(x)=(x-x3)2.

02

Step 2. Simplify the function

Apply the identity (a-b)2=a2-2ab+b2in the given function.

role="math" localid="1648549066913" f(x)=x2-2xx3+(x3)2=x-2x12+13+x23=x-2x56+x23

03

Step 3. Find the derivative

  • Apply the sum rule of derivative, (f+g)'(x)=f'(x)+g'(x)and the difference rule of derivative, (f-g)'(x)=f'(x)-g'(x).

localid="1648549080637" f'(x)=ddx(x)-ddx(2x56)+ddx(x23)

  • Apply the constant multiple rule of derivative, (kf)'(x)=kf'(x).

localid="1648549090521" f'(x)=ddx(x)-2ddx(x56)+ddx(x23)

  • Apply the power rule of derivative, localid="1648555968108" (xn)'=nxn-1.

localid="1648549175793" f'(x)=(1)-2(56x-16)+(23x-13)=1-53x-16+23x-13

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