Complete Question
The complete question is shown on the first uploaded image
Answer:
The derivative is [tex]v(r)' = \sqrt{\frac{D}{r} }[/tex]
The correct option is option 1
Explanation:
From the question we are told that
The equation of the speed of the wave of invasion is [tex]v(r) = 2 \sqrt{Dr}[/tex]
=> [tex]v(r) = 2 (Dr)^{\frac{1}{2} }[/tex]
=> [tex]v(r) = 2 * D^{\frac{1}{2} } r^{\frac{1}{2} }[/tex]
Here r is the reproductive rate and the D is the parameter qualifying dispersal
Generally the derivative of this speed is mathematically represented as
[tex]v(r)' = \frac{2}{2} * D^{\frac{1}{2} } * r^{-\frac{1}{2} }[/tex]
=> [tex]v(r)' = \sqrt{\frac{D}{r} }[/tex]
This derivative of the speed represents the rate of change of the invasive speed with respect to the the reproductive rate of an individual
