defining functions of s variables

Dear list,

As a newcomer to Maxima, I am trying to define a function of s
variables.

I know functions of multiple variables can be defined for example
as follows:

f(x,y) := x^1*y^2;

I can then calculate for example mixed partial derivatives as
follows:

diff(f(x,y), x, 1, y, 1);

Now my problem is that I want to be able to define functions of s
variables, where s is a parameter defined by the user.  For
example (in *non-maxima* notation):

f(x[1],...,x[s]) := x[1]^1*x[2]^2*...*x[s]^s;

                 := product(x[i]^i);

I then want to be able to compute certain partial derivatives of
the s-dimensional functions I define.

Is this at all possible with Maxima and what is the correct way
of doing this?

Thanks,
Bart

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