Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

A particle is moving along a hyperbola $ xy = 8. …

01:57

Question

Answered step-by-step

Problem 11 Easy Difficulty

If $ x^2 + y^2 + z^2 = 9, dx/dt = 5, $ and $ dy/dt = 4, $ find $ dz/dt $ when $ (x, y, z) = (2, 2, 1). $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Carson Merrill
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Carson Merrill

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

01:51

WZ

Wen Zheng

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 9

Related Rates

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Grace He
Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

04:22

Suppose $ 4x^2 + 9y^2 = 36…

01:36

Suppose $ y = \sqrt {2x + …

02:42

Evaluate dy/dx at the give…

0:00

Find the differential of t…

Watch More Solved Questions in Chapter 3

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50

Video Transcript

So in this problem, the first thing what we want to focus on is just looking at what we have. So we have X squared bus y squared a Z squared People's Nine and ultimately, this problem is helping us to do a better job of understanding related rates problems. So what we have here is, uh, we're gonna want to start by taking the derivative. So when we differentiate with respect to T that is on both sides, we'll end up getting two x times dx DT Class two I times d y d t class choosy. I'm dizzy E t. And we know this is equal to zero because we differentiate the nine. And with all this in mind, we end up seeing that X is equal toe one are actually X is equal to two. But we can factor out the two out of here. That makes it much easier. We know the X is equal to two. Why is equal to two z is equal to one so we can substitute those. We know that DX DT is equal to five d y d t is. You go to form and we're trying to find these e D t. So, since this we're multiplying by one here, we can just simplify that. That this is eight. This is 10. So 10 plus eight is 18. So now we can put this over here. When we subtract it, it'll be negative. 18. So what we've just done is found busy, bt, um, which essentially means we found the derivative of Z with respect to t. Um and we know that to be 18, a negative 18.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
151
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Caleb Elmore

Baylor University

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

04:22

Suppose $ 4x^2 + 9y^2 = 36, $ where $ x $ and $ y $ are functions of $ t $. (a…

01:36

Suppose $ y = \sqrt {2x + 1}, $ where $ x $ and $ y $ are function of $ t $, …

02:42

Evaluate dy/dx at the given points. $$2 y+5-x^{2}-y^{3}=0 ; \quad(2,-1)$$

0:00

Find the differential of the function. $$ H=x^{2} y^{4}+y^{3} z^{5} $$
Additional Mathematics Questions

01:39

1) Use a compass t0 d.JW & cirele oftadius $ ci. 1.) Cse a compass {0 dr…

01:49

1368
In the diagram, 4, B, C and D lie on the circle; cenlre 0. CO is par…

03:15

16.A Price-Demand The market research department Of a supermarket chain has …

01:44

item 4 to 8, refer to the figure; Which angles are vertical? LC and LB 2B an…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started