
Paint and Derivatives
A paint manufacturing company estimates that it can sell $\displaystyle g=f(p)$ gallons of pain at a price of $\displaystyle p$ dollars. What are the units of $\displaystyle \frac{dg}{dp}$?
How do I find units? Do I take the derivative and find $\displaystyle g'$? Even though its a simple question it stumps me. (Worried)

Notice that if we were to have the ratio:
$\displaystyle \frac{g}{p}$
The units would simplify to gallons per dollar.
Now notice that if you have:
$\displaystyle \frac{dg}{dp}$
That ratio is just a differential amount of paint over a differential amount of dollars. The units have not changed, they are still gallons per dollar, except this ratio shows how g changes when p changes.

So the units would be gallons per dollar? I thought I had to differentiate to find the answer.