I read the problem as follows: f(x) = 4x / sqrt(x^2 -8)
if it's not correct, let me know. Let me abbreviate f(x) as y, Then y = 4x * sqrt(x^2 -8)^(-1/2). Rewriting the problem in this way allows you to use the product rule instead of the (more complicated, IMHO) quotient rule.
Then fprime(x) = 4x * d(sqrt(x^2-8)^(-1/2)) + sqrt(x^2-8)^(-1/2) * d(4x)/dx. Simplifying, we get