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The meaning of dy/dx

  1. Jun 15, 2011 #1
    the meaning of "dy/dx

    1. The problem statement, all variables and given/known data
    I am unsure of what dy/dx means when used in derivatives. However, I do know that it is called the derivative operator and have been told its the derivative of y relative to x, but could someone elaborate this for me?


    2. Relevant equations
    an example equation might be dy/dx = x2 + 4x + 4


    3. The attempt at a solution
    I have been told that its called the derivative operator and that it is the derivative of y relative to x.
     
  2. jcsd
  3. Jun 15, 2011 #2
    Re: the meaning of "dy/dx

    I wasn't too sure if this would be considered a homework question. If someone could let me know so I can start posting in the correct section, that would be helpful. :smile:
     
  4. Jun 15, 2011 #3

    Mark44

    Staff: Mentor

    Re: the meaning of "dy/dx

    dy/dx is the derivative of y with respect to x, where y is assumed to be a differentiable function of x.

    dy/dx is not an operator - it is a function. d/dx is an operator that is applied to a differentiable function. A function takes a number as its input, and produces a number as its output. In contrast, an operator takes a function as its input, and produces a function as its output.
     
  5. Jun 15, 2011 #4
    Re: the meaning of "dy/dx

    To get my terminology straight, would a differential function be a derivative? please elaborate. Thank you.
     
  6. Jun 15, 2011 #5

    Mark44

    Staff: Mentor

    Re: the meaning of "dy/dx

    Do you mean "differentiable" function? If so, that's a function that can be differentiated; i.e., one that has a derivative. A differential is something different.
     
  7. Jun 15, 2011 #6
    Re: the meaning of "dy/dx

    Yes, exactly what I meant. Thank you
     
  8. Jun 15, 2011 #7

    Mark44

    Staff: Mentor

    Re: the meaning of "dy/dx

    There's something of a disconnect in the terminology that is used in English. To get the derivative of a function, we differentiate it (we don't derive it). If the function has a derivative, it is differentiable (not derivable). Go figure.
     
  9. Jun 15, 2011 #8
    Re: the meaning of "dy/dx

    That's because the concept of a differentiable function for functions with more than variable is more stringent than the simple existence of the partial derivatives.
     
  10. Jun 16, 2011 #9
    Re: the meaning of "dy/dx

    Fascinating. Therefore, what would one consider deriving a function?
     
  11. Jun 16, 2011 #10

    Mark44

    Staff: Mentor

    Re: the meaning of "dy/dx

    In the context of this thread (differentiation and the derivative), "deriving a function" has no meaning.

    In a different context, one can start from observations and derive a general formula, but this is unrelated to differentiation.
     
  12. Jun 16, 2011 #11
    Re: the meaning of "dy/dx

    Though my question was off-topic, thank you for answering it anyway.
     
    Last edited: Jun 16, 2011
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