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I'm trying to evaluate the partial derivatives of some function F[x,y] at some point, i.e.


However, for higher derivatives I find that it fails to evaluate the limit. On the other hand, if I use the Series function


It produces all the coefficients with no problem. My question is what is the difference between the two methods? what is Series assuming that I'm missing when I do it manually with the derivatives?

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What's a good example for F? I see no difference for, say, Sin[x] Exp[y]. – Michael E2 Aug 28 '14 at 11:29
@MichaelE2 Example Limit[D[BesselJ[c, x]/x, {x, 3}], x -> 0] vs Series[BesselJ[c, x]/x, {x, 0, 3}] The former times out while the latter gives the right result by looking at the coefficient of x^3 – Prastt Aug 28 '14 at 18:31
From the result of Trace, it seems Series[BesselJ[c, x]/x, {x, 0, 3}] is calculated by calculating Series[1/x, {x, 0, 3}] * Series[BesselJ[c, x], {x, 0, 3}]. – Silvia Sep 3 '14 at 0:14

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