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I have a lagrangian that is a function of the vector potential and I need to figure out the perturbed lagrangian by perturbing the vector potential. That is, I need to figure out Delta of Lagrangian of Vector Potential. Or how to I figure out:

dL = L(A+dA) - L(A) = ??? Say L = 2A + K

Would it work the same way differentials are taken? How do you figure out:

L(A+dA) ?????

Clearly I'm missing something here!!!