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edited Oct 13 at 15:03

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Consider the simple polynomial expansion of higher derivatives like powers of squares

Function@@{f,((ExpandAll[(x^2+y^2+z^2)^200]  /.
  { Plus->Inactive[Plus],Times->List,x_Symbol^n_:>{x,n}})/.
    {{x_Symbol,n_Integer}:> Inactive[D][f,{x,n}],
     {n_Integer,{ a_,m_Integer},b___List}:> n Inactive[D][f,a,b]})/.
  {Inactive[Plus][a___,b_Symbol,c___]:>Inactive[Plus][a,D[fInactive[D][f,b] ,c]}}

Consider the simple polynomial expansion of higher derivatives like powers of squares

Function@@{f,((ExpandAll[(x^2+y^2+z^2)^200]  /.
  { Plus->Inactive[Plus],Times->List,x_Symbol^n_:>{x,n}})/.
    {{x_Symbol,n_Integer}:> Inactive[D][f,{x,n}],
     {n_Integer,{ a_,m_Integer},b___List}:> n Inactive[D][f,a,b]})/.
  {Inactive[Plus][a___,b_Symbol,c___]:>Inactive[Plus][a,D[f,b] ,c]}}

Consider the simple polynomial expansion of higher derivatives like powers of squares

Function@@{f,((ExpandAll[(x^2+y^2+z^2)^200]  /.
  { Plus->Inactive[Plus],Times->List,x_Symbol^n_:>{x,n}})/.
    {{x_Symbol,n_Integer}:> Inactive[D][f,{x,n}],
     {n_Integer,{ a_,m_Integer},b___List}:> n Inactive[D][f,a,b]})/.
  {Inactive[Plus][a___,b_Symbol,c___]:>Inactive[Plus][a,Inactive[D][f,b] ,c]}}

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created Oct 12 at 17:51

Roland F

4.6k
1
2
12

Consider the simple polynomial expansion of higher derivatives like powers of squares

Function@@{f,((ExpandAll[(x^2+y^2+z^2)^200]  /.
  { Plus->Inactive[Plus],Times->List,x_Symbol^n_:>{x,n}})/.
    {{x_Symbol,n_Integer}:> Inactive[D][f,{x,n}],
     {n_Integer,{ a_,m_Integer},b___List}:> n Inactive[D][f,a,b]})/.
  {Inactive[Plus][a___,b_Symbol,c___]:>Inactive[Plus][a,D[f,b] ,c]}}