Chapter 2.7, Problem 34E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Invasive species often display a wave of advance as they colonize new areas. Mathematical models based on random dispersal and reproduction have demonstrated that the speed with which such waves move is given by the function
*r* is the reproductive rate of individuals and *D* is a parameter quantifying dispersal. Calculate the derivative of the wave speed with respect to the reproductive rate *r* and explain its meaning.

To determine

**To calculate:** The derivative of the wave speed with respect to the reproductive rate r and explain its meaning

Explanation

**1) Formula:**

Radical rule:

Chain rule:

Constant multiple rule:

**2) Given: **

**3) Calculation:**

Consider function,

Differentiate with respect to r,

By using constant multiple rule,

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