A paint manufacturing company estimates that it can sell gallons of pain at a price of dollars. What are the units of ?

How do I find units? Do I take the derivative and find ? Even though its a simple question it stumps me. (Worried)

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- Oct 13th 2009, 06:05 PMDarkestEvilPaint and Derivatives
A paint manufacturing company estimates that it can sell gallons of pain at a price of dollars. What are the units of ?

How do I find units? Do I take the derivative and find ? Even though its a simple question it stumps me. (Worried) - Oct 13th 2009, 06:14 PMAryth
Notice that if we were to have the ratio:

The units would simplify to gallons per dollar.

Now notice that if you have:

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. - Oct 13th 2009, 06:31 PMDarkestEvil
So the units would be gallons per dollar? I thought I had to differentiate to find the answer.