   Chapter 11.4, Problem 7E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 5-8, assume that x and y are differentiable functions of t. In each case, find d x / d t given that x =   5 , y   = 12 ,  and  d y / d t   = 2 . y 2 = 2 x y + 24

To determine

To calculate: The value of dxdt if y2=2xy+24 for x=5,y=12anddydt=2.

Explanation

Given Information:

The provided equation is:

y2=2xy+24

Formula used:

According to the chain rule, if f and g are differentiable functions with y=f(u) and u=g(x), then y is a differentiable function of x and:

dydx=dydududx

Calculation:

Consider the provided equation:

y2=2xy+24

Now, differentiate both sides with respect to t to get:

ddt(y2)=ddt(2xy)+ddt(24)

Now, use the chain rule:

dydx=dydududx

To obtain the derivative of x2andy2 as:

ddt(y2)=ddt(2xy)+

### 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

#### limx(12)x2= a) 0 b) 1 c) d) does not exist

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

#### Find for x = 3t2 + 1, y = t6 + 6t5. t4 + 5t3 4t3 + 15t2

Study Guide for Stewart's Multivariable Calculus, 8th

#### How does a full-text database differ from other databases?

Research Methods for the Behavioral Sciences (MindTap Course List) 