D(p)= 2sqrt 55-6p
find rate of change when p=5
All you do to find the rate of change is take the first derivative with respect to p, we know that:
$\displaystyle D(p) = 2\sqrt{55 - 6p} = 2(55 - 6p)^{\frac{1}{2}}$
So, the derivative would be:
$\displaystyle \frac{dD}{dp} = D'(p) = 2*\frac{1}{2}*\frac{1}{\sqrt{55 - 6p}}*-6$
$\displaystyle D'(p) = \frac{-6}{\sqrt{55 - 6p}}$
All you do is plug in p = 5.