Hey Everyone:
I was wondering if anyone could tell me where my error is.
Thanks
First of all, don't put equals signs where things aren't equal.
Specify where your derivative actually starts.
Second, it becomes much easier if you cancel the common factor of $\displaystyle v$.
So $\displaystyle y = \frac{v^3 - 2v\sqrt{v}}{v} = v^2 - 2\sqrt{v} = v^2 - 2v^{\frac{1}{2}}$.
Therefore $\displaystyle \frac{dy}{dv} = 2v - v^{-\frac{1}{2}} = 2v - \frac{1}{\sqrt{v}}$.