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Variation of a quantity

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Suppose I have such an equation:
[itex]A= f(B)[/itex]
so [itex]A[/itex] is a function of [itex]B[/itex].

Can I really use the fact that a variation of [itex]A[/itex] is like taking the differential of it?
[itex] \delta A= dA [/itex]

so that:

[itex] \delta A = \frac{d f(B)}{dB} \delta B[/itex]
?

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