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If there is a change of variables: $$(\vec x(t),t)\to (\vec u=\vec x+\vec a(t),\,\,\,v=t+b)$$ where $b$ is a constant.

Suppose I wish to write the following expression in terms of a gradient in $(\vec u, v)$ $$\nabla_\vec x f(\vec x,t)+{d^2\vec a\over dt^2}$$ How do I do that?

I suppose for the first term, $$f(\vec x, t)\to f(\vec u -\vec a, v-b)$$ I am not sure what to do with the second term though.


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