## Calculus, 10th Edition (Anton)

$\dfrac{du}{dv}=-\dfrac{\sqrt{u}}{\sqrt{v}}$
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 $\dfrac{u'}{2\sqrt{u}} = \dfrac{-1}{2\sqrt{v}}$ $u'=-\dfrac{\sqrt{u}}{\sqrt{v}}$