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I How was this expression differentiated?

  1. Jun 9, 2016 #1
    This is the derivative of an expression that contains terms of the form (partial derivatives)*differentials. Are you supposed to apply the product rule to the (partial)*differential terms? And with respect to what variable? question.png
    I've tried different ways but didn't get the right result, so if anyone could tell me just the procedure I would appreciate it very much.

    Thanks in advance
  2. jcsd
  3. Jun 9, 2016 #2

    Charles Link

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    It is a little tricky writing out all of the terms of the Taylor series for a function of two variables, ## f(x,y) ## in terms of ## f(x_o,y_o) ##, but if you proceed with the complete Taylor series to second order, you will get a term of mixed partials in the second derivative case. The ## d u d v ## is ## (x-x_o)(y-y_o) ## in the Taylor series...
    Last edited: Jun 9, 2016
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