# Math Help - Paint and Derivatives

1. ## Paint and Derivatives

A paint manufacturing company estimates that it can sell $g=f(p)$ gallons of pain at a price of $p$ dollars. What are the units of $\frac{dg}{dp}$?

How do I find units? Do I take the derivative and find $g'$? Even though its a simple question it stumps me.

2. Notice that if we were to have the ratio:

$\frac{g}{p}$

The units would simplify to gallons per dollar.

Now notice that if you have:

$\frac{dg}{dp}$

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.

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