Answer
$\dfrac{du}{dv}=-\dfrac{\sqrt{u}}{\sqrt{v}}$
Work Step by Step
In order to derivate this function you have to apply implicit differentation method.
First, take the function to it's f(v)=0 form
$ u^{1/2}+v^{1/2}-5=0$
Then derivate the whole equation. Rember the put u' every time you derivate u
$\dfrac{1}{2}u^{-1/2}+\dfrac{1}{2}v^{-1/2}=0$
Solve for a' and you have the answer
$\dfrac{u'}{2\sqrt{u}} = \dfrac{-1}{2\sqrt{v}}$
$u'=-\dfrac{\sqrt{u}}{\sqrt{v}}$
