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 $5/8$?

We have that
$$xy=40 \implies y = \frac{40}{x}. $$
Remember that
$$\frac{d}{dx}\frac{1}{x}  = - \frac{1}{x^2}$$
so
$$\frac{dy}{dx} = \frac{d}{dx}\frac{40}{x} = 40\frac{d}{dx}\frac{1}{x} =- \frac{40}{x^2}.   $$
Therefore we have, when $x = 8$, that
$$\frac{dy}{dx} = -\frac{40}{8^2} = -\frac{40}{64} = -\frac58. $$
