How to get (fg)' = f'g + g'f?

Question

I am new to Mathematica so the my questions might be pretty much at the pupil's level.

If I want to use differentiation to derive:

    (fg)' = f'g + g'f

How can I keep empty symbol f, g from been evaluated for derivative and get 0? For example if I use

    D[f g, x]

I immediately get 0 result. I guess it might be related to hold, but couldn't find out the correct way to get it work.

Try Dt[f g, x]. – J. M.'s missing motivation Jun 04 '13 at 16:02 — J. M.'s missing motivation, Jun 04 '13 at 16:02
Or perhaps, D[f[x] g[x], x]. – Michael E2 Jun 04 '13 at 16:05 — Michael E2, Jun 04 '13 at 16:05
Michael wins this round – Jacob Akkerboom Jun 04 '13 at 16:06 — Jacob Akkerboom, Jun 04 '13 at 16:06
Closely related: how to differentiate formally – Jens Jun 04 '13 at 16:11 — Jens, Jun 04 '13 at 16:11

score 8 · Answer 1 · answered Jun 04 '13 at 16:24

8

Some alternatives (picked from the comments):

D[f[x] g[x], x]

Dt[f g, x]

f[#] g[#] &'

answered Jun 04 '13 at 16:24

Szabolcs

Great it is solved! – JimmyLin Jun 04 '13 at 17:09
Thanks! Didn't think of something like f[#] g[#] &'. – Silvia Jun 04 '13 at 19:43

1 Answers1