Chapter 4.5, Problem 75E

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

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Demand Solve the demand function in Exercise 73 for p. Use the result to find dp/dx. Then find the rate of change when p = $10. What is the relationship between this derivative and dx/dp? To determine To calculate: The value of demand function by using the result dpdx for the demand function which is approximated by x=ln1000p and to explain the same for the change of a price of$10 if the demand function is as follows:

Explanation

Given information:

The provided function is x=ln1000p and graph is,

Formula used:

The derivative of e raised to a function is ddxeu=eududx.

Constant multiple rule of derivative of function f(x) is f(cx)=cf(x) where, c is constant.

Calculation:

Consider the function x=ln1000p,

Rewrite the function with rational exponent,

x=ln1000pex=1000pp=1000ex

The derivative of function p=1000ex is,

dpdx=ddx(1000ex)=

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