   Chapter 3.9, Problem 10E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Suppose 4x2 + 9y2 = 36, where x and y are functions of t.(a) If d y / d t = 1 3 , find dx/dt when x = 2 and y = 2 3 5 (b) If dx/dt = 3, find dy/dt when x = –2 and y = 2 3 5

To determine
dxdt  when x=2 and y=235 with dydt=13
Explanation

Given:

The given values are dydt=13 and x=2 and y=235.

Formula used:

Chain rule:dydx=dydududx

Calculation:

Since 4x2+9y2=36  where x  and y are the function of the variable t.

Therefore, x and y changes when the variable t changes.

Since dydt=13.

Obtain dxdt when x=2 and y=235.

Differentiate the function 4x2+9y2=36 with respect to the variable t both sides.

ddt(4x2+9y2=36)=ddt(26)4ddt(x2)+9ddt(y2)=04(2x)dxdt+9(2y)dydt=0(8x)d

(b)

To determine
dydt when x=2 and y=235 with dxdt=3.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Problems 39 – 44, solve each inequality and graph the solution. 41.

Mathematical Applications for the Management, Life, and Social Sciences

#### Change 430 g to mg.

Elementary Technical Mathematics

#### Find f(x) if f(x)=1x2 and f(2) = 0. a) 1x+12 b) 1x12 c) 3x3+38 d) 3x338

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 