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Derivative wrt a constant?

  1. Feb 11, 2012 #1
    This is coming up a lot in some of my thermo HW, so I'm a little confused about whether or not I'm thinking correctly.

    Suppose I have a function [itex]f = f(x,a)[/itex]

    where a is some constant. If I take the derivative of f wrt to a, what do I get?

    The derivative tells you the change in the function due to some small change in a quantity, so if I want to know how f changes with respect a, how does one interpet this?

    a can't change, so it seems that f can't change wrt to a, so [itex] df/da = 0[/itex] seems like the only thing that makes sense, but does it actually?

    For example, if [itex]f(x,a) = ax + a[/itex], then should [itex]df/da = 0[/itex] or [itex]df/da = x + 1[/itex] ?
  2. jcsd
  3. Feb 11, 2012 #2


    Staff: Mentor

    It doesn't make any sense to take a derivative wrt a constant. So IOW, taking the derivative of f wrt to a is undefined.
  4. Feb 11, 2012 #3


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    Homework Helper

    As Mark44 said, the question you asked doesn't mean anything, so it's hard to know what you are really having problems with.

    Can you post a particular thermo problem where you think you need to differentiate wrt a constant? That might get a more helpful answer than "this doesn't mean anything".
  5. Feb 11, 2012 #4
    Don't worry about 'a' being a constant, if it appears in the function definition, then it is a 'variable' as any other.
    Think of it as a parameter if it helps
    For instance, suppose f(x, a) is a function that gives you for x being the height, how long will a mass takes to hit the ground. 'a' would be the constant 'g'
    Obviously, this 'constant' isn't so constant, it will vary slightly on earth, and a lot more if you don't stay on earth, you could become interested in asking yourself, just how much do different values of g change the value of f for some fixed x...
  6. Feb 11, 2012 #5


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    Science Advisor

    Hey dipole and welcome to the forums.

    One thing that you might want to think about is the situation y = c for a constant c. Now lets say our system is two dimensional (x,y). What is dy/dx? How about dx/dy?
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