I’m trying to make a sum with derivatives of an arbitrary number of parameters. E.g. for a vector
function F(x,y)=[exp(x^3 y) - 1, y^2 - 5xy] I’d like to calculate expressions like first derivative multiplied on something.

I tried

n := 2;
xvars := seq(x[i], i = 1 .. n);
yvars := seq(y[i], i = 1 .. n);
F := (x, y) -> [exp(x^3 *y) - 1, y^2 - 5*y*x];
seq(sum(diff(F(xvars)[i], xvars[j])*yvars[j], j = 1 .. n), i = 1 .. n);

and got 0,0. And diff(F(xvars)[1], xvars[1]) it finds correctly. Seems like Maple is differentiating with respect to xvars[j] rather than xvars[1] and xvars[2]. Changing diff on D gives another but also incorrect answer.

How to do it in general?

I’d like to understand how to do it with many variables and nested sums.