   Chapter 3.9, Problem 9E ### 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 y = 2 x + 1 , where x and y are functions of t.(a) If dx/dt = 3, find dy/dt when x = 4.(b) If dy/dt = 5, find dx/dt when x = 12.

(a)

To determine

To find: dydt when x=4, with dxdt=3.

Explanation

Given:

The given values are dxdt=3 and x=4.

Formula used:

Chain rule: dydx=dydududx .

Calculation:

Since y=2x+1 where x and y are function of variable t.

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

Since dxdt=3.

Obtain dydt when x=4.

Differentiate the function y=2x+1 with respect to the variable t.

dydt=ddt(2x+1)=ddx(2x+1)dxdt[Qdydx=dydududx]=d<

(b)

To determine

To find: dxdt when x=12 with dydt=5.

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