vector differentiation by looping in Mathematica

Hi all

I need to take the derivative of a row vector w.r.t. another row vector using Mathematica.

e.g. take the derivative of {a1,a2,....an} w.r.t {b1,b2,....,bk}

But each element in the first row vector is very large and it takes too much ram to run.

I am trying to do it by looping, i.e. take the elements in the first row vector one at a time to take the derivative w.r.t. the second row vector.

Based on what I know, the command "Do" can only take the elements from a true matrix, which cannot only be a vector. Also, I cannot specify the row vector in the way that each row (of a matrix) is only a scalar. i.e. {{a1},{a2},....{an}} because each element is very large, and it takes lots of ram to change just a tiny thing.

Does anyone know how to take the elements in the first row vector one at a time to take the derivative w.r.t. the second row vector?

Thanks a lot!