Differentiation of Vector Equation

Question

Is it possible to get symbolic derivatives of equations with vectors as arguments without specifying every vector element explicitly.

Something like

f[A_Vector, B_Vector] := Dot[A, B]
D[f[a, b], a[[1]]]

possible duplicate of Is it possible to do vector calculus in Mathematica? — Sjoerd C. de Vries, Sep 30 '15 at 06:43

Karsten7 · Answer 1 · 2014-07-18T21:10:14.343

1

The vector elements just need to be specified symbolically. This can be done implicitly by specifying the dimension of the vectors.

f[a_,b_,n_]:=Dot[Table[Subscript[a, i],{i,1,n}],Table[Subscript[b, i],{i,1,n}]]
D[f[a, b, 5], Subscript[a, 1]]

Subscript[b, 1]

Which looks nicer in the notebook: enter image description here

edited Jul 18 '14 at 21:10

answered Jul 18 '14 at 20:44

Karsten7

Yes, this works of course but I would like to get the result in terms of the input vectors a and b. – paw Jul 19 '14 at 14:18
@paw May you add an example of the desired output for clarification. – Karsten7 Jul 19 '14 at 15:46

1 Answers1