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Partial differential derivation

  1. Mar 2, 2017 #1
    1. The problem statement, all variables and given/known data
    Hi guys, I am having a problem, knowing where to start with this question. Before I spend trying derive the partial derivative chain rule from first principles I would just like to know if this is what this questions is asking. If it is not asking that, how do I go about solving it.
    upload_2017-3-3_2-20-29.png


    2. Relevant equations


    3. The attempt at a solution
    I have not shown solution beacuse I am unware where to start
     
  2. jcsd
  3. Mar 3, 2017 #2
    I have mange to come up with one solution, which: If I think that y,x are all functions of t. Then I could say: dx=dx/dt *dt and dy=dy/dt *dt sub in to the total differential and get ##\partial{df}{dx}\frac{dx}{dt}*dt+\partial{df}{dy}\frac{dy}{dt}*dt## I am just unsure of this method, I feel like I am cheating, any advice?
     
  4. Mar 3, 2017 #3

    Mark44

    Staff: Mentor

    This -- ##\partial{df}{dx}\frac{dx}{dt}*dt+\partial{df}{dy}\frac{dy}{dt}*dt## -- doesn't make any sense. The expression ##df## is defined (it's the differential of f), but this one ##\partial f## doesn't mean anything.

    You have f(x, y) where x is a function of t and y is another function of t. This means that f is ultimately a function of t, albeit one with two parameters.
     
  5. Mar 4, 2017 #4
    Sorry for the bad latex, I did eventually solve the problem. I was over thinking the problem and thought I had to derive partial chain rule from first principles, which I on my way to doing, by deriving the non partial chain rule. As a question, am I on the right lines if I derive chain rule from first principles then, then apply the same method to partial, would I be able to derive the above formula?
     
  6. Mar 4, 2017 #5

    Mark44

    Staff: Mentor

    Which formula above do you mean?
     
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