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Mixing units with functions or derivatives?

  1. Jul 16, 2015 #1
    How do you correctly use units when writing derivatives and functions in math?


    A car goes 17miles per gallon, so a function m with the equation m(g)=17g describes the distance it can go with g gallons.

    And the derivative dm/dg = 17 miles/gallon.

    Question: could you write the equation as m(g)=17(miles/gallon)*g or is that incorrect?
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  3. Jul 16, 2015 #2


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    Yes. That would be correct.
  4. Jul 16, 2015 #3


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    Your question is confusing. It looks like you are asking is m(g)=17g correct, if m(g)=17g, except you are writing a label for 17?
  5. Jul 16, 2015 #4
    When you are defining a variable, you can give it its unit right away or not.
    So if you say ##m## is the distance the car can drive, then the variable ##m## has already contained the unit, maybe miles. So you should write:$$m=17mile/gallon\cdot g.$$You can see here my ##g## has also contained its unit: gallon, but 17 not, so then I write 17mile/gallon in the equation.
    By the way, we seldom use ##m## to represent the distance because it is more often used to say mass, but it doesn't matter while it just depends on one's habits.
  6. Jul 17, 2015 #5


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    It should be evident that if m is a distance, measured in miles, and g is a quantity of gasoline, measured in gallons, then in order that "m (miles)= k g(gallons) make sense, k must be in "miles per gallon" so that (k miles/gallon)(g gallons)= kg miles.
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