Download the App!

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

Question

Answered step-by-step

Suppose $ y = \sqrt {2x + 1}, $ where $ x $ and $ y $ are function of $ t $, (a) If $ dx/dt = 3, $ find $ dy/dt $ when $ x = 4. $(b) If $ dy/dt = 5, $ find $ dx/dt $ when $ x = 12. $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Carson Merrill

Numerade Educator

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

05:12

Alex Lee

02:47

Chris Trentman

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 9

Related Rates

Derivatives

Differentiation

Ally J.

March 29, 2021

when i solved the problem i also got 25

the book states the answer is 25

Sharieleen A.

October 26, 2020

Finally, the answer I needed, thanks Alex L.

Catherine A.

That was not easy, glad this was able to help

Missouri State University

Campbell University

Baylor University

Idaho State University

Lectures

04:40

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.

44:57

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.

0:00

Suppose $ y = \sqrt {2x + …

04:19

Supposey =square r…

04:22

Suppose $ 4x^2 + 9y^2 = 36…

01:14

Suppose y = 2x + 1…

01:04

Suppose y = 2x + 1 , where…

02:00

04:09

Suppose $y=\sqrt{2 x+1},$ …

02:09

02:11

Find $ dy/dx $,

$ …

02:13

If $ x^2 + y^2 + z^2 = 9, …

00:42

(a) Find the differential …

02:36

Suppose $4 x^{2}+9 y^{2}=3…

03:13

02:48

Find the differential $d y…

02:20

Find the differential dy o…

So given that Y. Is equal to the square root of to act parts one. Okay. And we know that expire function of T. We want to find, we know that DX DT is three D. Y. D. T. S. Um We want to find the right to an X. Equals four. So what we're gonna do first is differentiate this with respect to T. So we'll have E. Y. D. T. Is equal to one half two X. Plus one to the negative one hacks. Um Thanks to the way and then we have dX DT. Then when we consider the fact that the X 80 is three we'll have this all equal three. So then when X. Is equal to for what we end up getting is um that when actually people before we get that Dy DT is three over route nine. Mhm. And we know through ever and it's just gonna be one that's because this is the square root of nine but it's in the denominator so I'm not getting one.

View More Answers From This Book

Find Another Textbook

University of Nottingham