Answer
$y'=-\dfrac{3}{2\sqrt{(3x+5)^3}}.$
Work Step by Step
$y=\dfrac{1}{\sqrt{3x+5}}=(3x+5)^{-\frac{1}{2}}$
Using the Chain Rule:
$u=(3x+5)$; $\dfrac{du}{dx}=3$
$\dfrac{dy}{du}=-\dfrac{1}{2\sqrt{u^3}}$
$\dfrac{dy}{dx}=\dfrac{dy}{du}\times\dfrac{du}{dx}=(3)(-\dfrac{1}{2\sqrt{(3x+5)^3}})=-\dfrac{3}{2\sqrt{(3x+5)^3}}.$
