Find the value of $dy/dx$ at $x=8$ 
Given that variables $xy=40$, find $dy/dx$ at $x=8$.

I used $40/8$ to get $y=5$.
So why is the answer $-5/8$ and not $5/8$?

Rewriting your equation you get:
$$y=\frac{40}{x}$$
Differentiating:
$$\frac{d}{dx}(\frac{40}{x})=\frac{d}{dx}(40x^{-1})=-40x^{-2}=-\frac{40}{x^2}$$
Pluggin in $x=8$
$$\implies -\frac{40}{64}=-\frac{5}{8}$$
