How to handle functions with varying number of arguments

Question

Suppose I have a function that depends on variables $x_1, ... , x_n$. For concreteness I may have $f(x) = v \cdot x$, with $v$ a certain vector.

Now I want to do certain operation with this function, for example to compute its gradient.

I would like to write a mathematica code that works for any n. Thus, I cannot write something like

f[x1_,...,xn_]:= (any clever way to write v . x);

because that would not work for another n: I have to manually write the new simbols x1,...,xn'.

Also, the following would not work:

f[x_]:= v . x;

because then I would not be able to use Derivative, as f is now a function of a single argument (a list), and it is impossible to get the derivative with respect to x[[2]] say. (Right?)

What is the best design to work with this kind of problems?

Of course Mathematica functions can have an arbitrary number of arguments. But why not just let the function take a list, which is treated as a single argument? f[list_List]:=Total[list]. Using the multi-argument notation, this would be f[x___]:=Total[{x}]. Here I put x between curly braces again to make a list out of it. So it's really the same thing as a function taking a list-argument. The difference is only notation, nothing else. This should make it easier for you to think about the problem. — Szabolcs, Sep 09 '17 at 12:56
But how would you compute the derivative with respect to the i-th argument? — giulio bullsaver, Sep 09 '17 at 14:14
D was enhanced in V11.1 to help with this sort of problem. Take a look at this Wolfram Blog article — m_goldberg, Sep 09 '17 at 18:13

How to handle functions with varying number of arguments

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