How can I determine the double derivative of a function $f:R^n \to R$?

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A function $f:R^n \to R$ belong to $C^2$. So $Df$ will be a matrix of order "1 by n". So now the range set of function $Df$ will be all row matrix of order "1 by n" while domain set will remain same(set of all column matrix of order "n by 1"). Then how can I handle this function? How would I determine $D^2f$? Can anyone please help me out?