Originally Posted by
Moo Do you know about conjugates ?
This is mostly about this identity : $\displaystyle (a-b)(a+b)=a^2-b^2$
So when you have a square root that's disturbing you, you can multiply by its conjugate, because it will square the square root.
For example, the conjugate of $\displaystyle 3-\sqrt{x}$ is $\displaystyle 3+\sqrt{x}$
So the trick (that you can use in many situations) is to multiply by $\displaystyle 1=\frac{3+\sqrt{x}}{3+\sqrt{x}}$
------------------------------------
Otherwise, your derivative (not the answer) is correct.
Remember that l'Hospital's rule is used in situations $\displaystyle \frac \infty \infty$ or $\displaystyle \frac 00$