## Question about variational derivative

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

$W_{mag}=\int_{V}\frac{1}{2}H.Bdv$

Now intuitively

1) $H=\frac{d W_{mag}}{dv d B}$

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

2) $H=\frac{\partial W_{mag}}{\partial B}$
3) $H=\frac{\delta W_{mag}}{\delta B}$ ( 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.
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 Tags magnetic energy, partial derivative

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