   Chapter 11.3, Problem 55E ### 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

# Advertising and sales Suppose that a company’s sales volume y (in thousands of units) is related to its advertising expenditures x (in thousands of dollars) according to x y − 20 x + 10 y = 0 Find the rate of change of sales volume with respect to advertising expenditures when x = 10 (thousand dollars).

To determine

To calculate: The rate of change of sales volume with respect to advertising expenditures when x=10 if sales volume y is related to its advertising expenditures x according to the equation, xy20x+10y=0.

Explanation

Given Information:

Sales volume y (in thousands of units) is related to its advertising expenditures x (I thousands of dollars) according to the equation, xy20x+10y=0.

Formula used:

According to the product rule of derivatives,

ddx(uv)=udvdx+vdudx

Calculation:

The sales volume y is related to its advertising expenditures x according to the equation,

xy20x+10y=0

Now, the rate of change of sales volume with respect to advertising expenditures is given by dydx.

Now, differentiate both sides with respect to x as,

ddx(xy20x+10y)=ddx(0)

Now, use the product rule of derivatives,

ddx(uv)=udvdx+vdudx

To obtain the derivative of xy as,

ddx(xy)20dxdx+10dydx=0xdy

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