Loops involving derivatives to different orders.

Questions
1

Hi, I’ve had one course in Mathematica, earlier in my math-education, but it was very basic.

Now, I’m trying to find a way to compute a list where I get the derivative up to, and including, the derivative of order n, for each polynomial in another list that I have defined.

Let me illustrate:

For[k = 1, k <= Length[specifiednus], k++,Table[D[Outpt[[k]],{t,i}],{i,0,specifiednus[[k]]}]]

This does not work.

This does work:

Table[D[Outpt[[1]],{t,i}],{i,0,specifiednus[[1]]}]

Output is a list of polynomials. “specifiednus” specifies which order of the derivative you want. Let’s say specifiednus[[1]] = 2. That means that I want the original polynomial, and it’s first two derivatives.

So, I want all of the derivatives up to the degree specified by the list “specifiednus”, for each polynomial, and the original polynomials, in one list.

Any suggestions?

Best,

Ben

2

Hi Benjamin,

Something like this?

ClearAll@x;
polys = Array[x^# &, 4]
(* {x, x^2, x^3, x^4} *)

orders = {0, 1, 1, 2};

derivs = MapThread[D[#1, {x, #2}] &, {polys, orders}]
(* {x, 2 x, 3 x^2, 12 x^2} *)

Not sure what you mean by “and the original polynomials, in one list”? Maybe

polysAndDerivs = MapThread[{#1, D[#1, {x, #2}]} &, {polys, orders}]
(* {{x, x}, {x^2, 2 x}, {x^3, 3 x^2}, {x^4, 12 x^2}} *)

Edit

Oops, I missed this bit “the derivative up to, and including, the derivative of order n”

derivList[f_, n_] := Table[D[f, {x, i}], {i, 0, n}];
MapThread[derivList[#1, #2] &, {polys, orders}]
(* {{x}, {x^2, 2 x}, {x^3, 3 x^2}, {x^4, 4 x^3, 12 x^2}} *)
3

Like this perhaps?

outpt = {p1[x], p2[x], p3[x], p4[x]}
specifiednus = RandomInteger[{1, 5}, 4]
dat = Transpose[{specifiednus, outpt}]
Function[{j, u}, Table[Derivative[i][u], {i, 1, j}]] @@@ dat

Edit:

This is better

outpt = {p1[x], Sin[x], p3[x], x^n}
specifiednus = RandomInteger[{1, 8}, 4]
dat = Transpose[{specifiednus, outpt}]
Function[{j, u}, Table[D[u, {x, i}], {i, 1, j}]] @@@ dat;
% // ColumnForm
4

Thanks guys, it seems like this

Table[D[Outpt[[k]],{t,i}],{i,0,specifiednus[[k]]}],{k,1,Length[Outpt]}];
upcat = Flatten[cat];

Did the trick.

5

I got the tips from some other forum, I believe stack-exchange or something similar.

6

Or

Inner[Table[D[#1, {x, i}], {i, #2}] &, outpt, specifiednus, List]