You're derivative is equivalent to what they have except at one point. The derivative of the inverse cosine has a negative on it, not a positive, turning your answer to:
Then you take the second term and multiply it by to get:
Then you put everything together to get:
We know that the thing inside the square root can factor:
From there, you simply recognize that:
To get:
This will then give:
So, the values are:
c = 7
m = -1
n = 7
p = 1/2