Question about variational derivative

Hassan2

I have a question as to what notation should I use for the following derivation ( I have no background on calculus of variation ):

In linear media , the stored energy in a given volume is given by

[itex]W_{mag}=\int_{V}\frac{1}{2}H.Bdv[/itex]

Now intuitively

1) [itex]H=\frac{d W_{mag}}{dv d B}[/itex]


But this is not the way they write it, instead one of the following notations are used:


2) [itex]H=\frac{\partial W_{mag}}{\partial B}[/itex]
3) [itex]H=\frac{\delta W_{mag}}{\delta B}[/itex] ( dv is missing)

What is the right notation for equation 1 ?


Thanks.

Edit: In 1) it is assumed that B inside the infinitesimal volume (dv) changes to B+dB while outside dv it remained constant.