Finding the vector field of the given potential function Given the potential function

$$f(V) = \cos (|X|^2), \quad X = (X_1, \dots, X_n)$$

find the vector field $V(X).$
I'm not really use to do this kind of question, usually they ask the other way around: finding the potential function. Also, usually it is defined in terms of $(x, y)$ or $(x,y,z)$ and I can differentiate for each of these variables, but this time it's $(X_1, \dots, X_n)$, how to differentiate it?
I'm just doing this:
$${df\over dX_i} = -2 X_i \sin (X_i^2)$$  
for  $i = 1,\dots,n$. 
So what to do next? I need your help. Thanks in advance.

$$
 F(x) = \cos \left( \theta(x) \right) = \cos \left( \sqrt{\sum_{k=1}^{n}x_{k}^{2}} \right)
$$
$$
\nabla F = 
\left[ \begin{array}{c}
  \partial_{x_{1}} \cos \left( \theta(x) \right) \\
  \partial_{x_{2}} \cos \left( \theta(x) \right) \\
  \vdots \\
  \partial_{x_{n}} \cos \left( \theta(x) \right) \\
\end{array} \right]
%
=
%
\frac{1}{\lVert x \rVert}
\left[ \begin{array}{c}
  -x_{1} \sin \left( \theta(x) \right) \\
  -x_{2} \sin \left( \theta(x) \right) \\
  \vdots \\
  -x_{n} \sin \left( \theta(x) \right) \\
\end{array} \right]
$$
