Given that I need to determine the Taylor expansion of a multi-variable function $f: \mathbb{R}^m \to \mathbb{R}^n$. Is that neccessary that $f$ belongs to the functional space of functions which are partial derivative to the $k$-th order for every combination of order of deriving?
I think that the answer is yes, but something just feels off. And I'm just asking this to verify. Please help me.