   Chapter 11.4, Problem 8E ### 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   = 1 2 ,   a n d   d y / d t   = 2 . x 2 ( y − 6 ) = 12 y + 6

To determine

To calculate: The value of dxdt if x2(y6)=12y+6 for x=5,y=12anddydt=2.

Explanation

Given Information:

The provided equation is:

x2(y6)=12y+6

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:

x2(y6)=12y+6

Now, use the chain rule:

dydx=dydududx

To obtain the derivative of x2andy2 as:

ddt(x2(y6))=ddt(12y)+ddt(6)2x(y6)dxdt<

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