#### Answer

$y' = 4x^{-1/2}+\dfrac{9}{2}x^{-1/4}$

#### Work Step by Step

In order to derivate this function you have to apply the power rule:
$\dfrac{d}{dx}(x^n)=nx^{n-1}$
But first let's rewrite the function
$y = 8x^{1/2}+6x^{3/4}$
$y' = 8(1/2)x^{-1/2}+6(\dfrac{3}{4})x^{-1/4}$
$y' = 4x^{-1/2}+\dfrac{9}{2}x^{-1/4}$