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Math Help - Paint and Derivatives

  1. #1
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    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.
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  2. #2
    Super Member Aryth's Avatar
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    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.
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  3. #3
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    So the units would be gallons per dollar? I thought I had to differentiate to find the answer.
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