   Chapter 7.4, Problem 68E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Shareholder’s Equity The shareholder’s equity z (in millions of dollars) for Skechers from 2009 through 2013 can be modeled by z = 0.105 x + 0.339 y + 257 Where x is the sales (in millions of dollars) and y is the total assets (in millions of dollars). (Source: Skechers U.S.A., Inc.)Find ∂ z / ∂ x and ∂ z / ∂ y .Interpret the partial derivatives in the context of the problem.

(a)

To determine

To calculate: The value of zx and zy from the shareholder equity function that is modelled by z=0.105x+0.339y+257 for the Skechers from 2009 through 2013.

Explanation

Given information:

The provided shareholder equity function z=0.105x+0.339y+257 for the Skechers from 2009 through 2013. Where, x is the sales and y are the total assets.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided function is,

z=0.105x+0.339y+257

Partially derivative of the function z=0.105x+0.339y+257 with respect to x.

zx=x(0.105x+0.339y+257)=0.105x(x)+0.339yx(1)+x(257)=0

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