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I am studying the Galilean group of transformations and I'm not sure how to transform the Nabla operator.

Consider the 2 transformations:

(x,t)->(x+s,t)

(x,t)->(Dx,t)

and the expression "nabla (x)"

where D is a matrix and x, s are vectors

I am pretty sure that I have to substitute x+s or Dx for x, but what about the nabla operator. How am I supposed to transform it?

And another question: If I have a transformation which somehow changes time (t->t+T), and a second derivative dx(t)/dt of a function, then does the derivative change its variable from t to t+T [dx(t+T)/d(t+T)] under the transformation or not?

thanks a lot in advance

best regards, marin