# Math Help - Rate of change in demand

1. ## Rate of change in demand

D(p)= 2sqrt 55-6p

find rate of change when p=5

2. All you do to find the rate of change is take the first derivative with respect to p, we know that:

$D(p) = 2\sqrt{55 - 6p} = 2(55 - 6p)^{\frac{1}{2}}$

So, the derivative would be:

$\frac{dD}{dp} = D'(p) = 2*\frac{1}{2}*\frac{1}{\sqrt{55 - 6p}}*-6$

$D'(p) = \frac{-6}{\sqrt{55 - 6p}}$

All you do is plug in p = 5.