# How to iteratively display the nth derivative?

I am new to Mathematica, but not so new to programming. What I'd like to do in Mathematica (not using an API) is to display on each line, the nth derivative of a function, e.g. for n = 1..10. Is there a way to accomplish this in Mathematica? (without explicitly typing the command for each derivative of course. e.g. does Mathematica have iterative constructs to do this).

• Column[D[Sin[x] Log[x], {x, #}] & /@ Range[10]] ? Aug 18 '12 at 16:49
• @b.gatessucks looks good; how about: Print@D[Sin[x] Log[x], {x, #}] & ~Array~ 10; ? Aug 18 '12 at 16:51
• ...or Scan[Print[D[Sin[x] Log[x], {x, #}]] &, Range[10]] or Do[Print[D[Sin[x] Log[x], {x, k}]], {k, 10}]. Aug 18 '12 at 16:56
• @J.M. not enough infix. :^) Aug 18 '12 at 16:57
• @Mr.Wizard, but I am forced to think when reading infix... ;) Aug 18 '12 at 16:59

Avoiding cleverness as much as possible, you can just use a Do loop:

Do[Print[D[Exp[-a*x], {x, n}]], {n, 0, 10}]


Or for example

Grid@(List@D[Exp[-a*x], {x, #}] & /@ Range[0, 10])


etc

"Iteratively differentiate" cries out Nest[] to me,....

Print /@ NestList[D[#, x] &, Exp[-a*x], 10];


Or substitute CellPrint@ExpressionCell[#, "Output"] & for Print for different styling.