Question

Differentiate the function. $f(x)=x^{3 / 2}+x^{-3}$

   Differentiate the function.
$f(x)=x^{3 / 2}+x^{-3}$
Single Variable Calculus: Early Transcendentals
Single Variable Calculus: Early Transcendentals
James Stewart,… 9th Edition
Chapter 3, Problem 11 ↓
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Differentiate the function. $f(x)=x^{3 / 2}+x^{-3}$
Close icon
Play audio
Feedback
Powered by NumerAI
Jennifer Stoner Ivan Kochetkov
Kathleen Carty verified

Gregory Higby and 75 other educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Recommended Videos

-
differentiate-the-function-fxleftx2frac1x2right3

Differentiate the function. $$f(x)=\left(x^{2}+\frac{1}{x^{2}}\right)^{3}$$

Calculus: One Variable

The Derivative; The Process of Differentiation

The Chain Rule

differentiate-fxleftfracsqrtx21right3-2

Differentiate. $$f(x)=\left(\frac{\sqrt{x}}{2}+1\right)^{3 / 2}$$

Calculus and Its Applications

The Derivative

Some Rules for Differentiation

hw-3-section-235

HW 3 Section 2.3#5


*

Transcript

-
00:01 So what you want to do with this problem is you have x to the three halves plus x to the negative third.
00:11 So the theme is that whenever you're trying to take the derivative of some constant times x to the n power, it's going to equal the constant times the exponent.
00:23 So we call it the coefficient times the exponent.
00:26 And then you subtract one from your exponent.
00:28 So in this problem, you just have two pieces because that plus just goes along for the ride...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever