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**Jiftim** Let $\displaystyle V$ be the collection of all functions whose domain is $\displaystyle R^2

$ and differentiable on the domain. Also, let $\displaystyle U$ be the

collection of all functions whose domain is $\displaystyle R^2$and continuous on the domain.

$\displaystyle D: V\rightarrow U$

$\displaystyle f(x) \mapsto Df(x)=f'(x) $

I know that I need to prove for any $\displaystyle \vec{u}\epsilon U$, $\displaystyle D\vec{v}=\vec{v}\boldsymbol{'}=\vec{u}$ for some $\displaystyle \vec{v}\epsilon V$ but I dont know how to go about writing the proof. Can anyone help me at least get a start on it? I'm sure I can figure it out with the proper hint.

Also, every example I find online, has $\displaystyle f(x)$ equaling some function (i.e. $\displaystyle f(x)=x^2$). In my case, I dont have a specific function so that is why I am stuck and confused.