How was this expression differentiated?

  • #1

Main Question or Discussion Point

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?
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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
 

Answers and Replies

  • #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...
 
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