Chapter 9.6, Problem 45E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# Demand If the demand for q units of a product priced at $p per unit is described by the equation p = 100 2 q + 1 find the rate of change of p with respect to q. To determine To calculate: The rate of change of p with respect to q. The demand for q units of a product priced at$p per unit is described by the equation p=1002q+1.

Explanation

Given Information:

The demand for q units of a product priced at \$p per unit is described by p=1002q+1.

Formula used:

The power rule of differentiation,

ddxxn=nxnâˆ’1

Calculation:

Consider the provided function,

p=1002q+1

Rewrite the function,

p=100(2q+1)âˆ’1/2

Consider (2q+1) to be u,

p=100uâˆ’1/2

Differentiate both sides with respect to p,

dpdq=ddq(100uâˆ’1/2)

Simplify using the power rule,

dpdq=100â‹…âˆ’12â‹…uâˆ’12âˆ’1â‹…dudq=âˆ’50uâˆ’3/2dudq

Substitute (2q+1) for u,

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