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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

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 f ( r ) =   2 D r , where 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:

f'r=ddr(fr)

Radical rule:

ddrx=12x

Chain rule:

ddx(fgx=f'gx*g'(x)

Constant multiple rule:

ddxCfx=Cddx(fx)

2) Given: fr=2Dr

3) Calculation:

Consider function,

fr=2Dr

Differentiate with respect to r,

f'r=ddr(2Dr)

By using constant multiple rule,

f'r=2ddr(D

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