Using Jet to compute Taylor coefficients of multivariate function

[LeanderK]

I have the following problem, I have a family of functions fs(x) = (f_1(x0), ...., f_n(x_0)) and want to get the taylor coefficients for each of them.

So, focussing on a single f: R^N -> R, I thought about using jet as it talks a lot about taylor polynomials. But I struggle to use it!
I find the documentation very hard to understand tbh. How can I obtain the taylor coefficients? I think i understood it for a univariate function but not for a multivariate function.