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Derivatives in replacement rules

• To: mathgroup at smc.vnet.net
• Subject: [mg125733] Derivatives in replacement rules
• From: Yi Wang <tririverwangyi at gmail.com>
• Date: Fri, 30 Mar 2012 04:36:42 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi, all,

When I am using the following replacement rule:

b[t] c[t] a'[t] /. b_ a_'[t] -> D[b, t]

I would expect to get D[b[t]c[t], t] = b'[t]c[t] + c'[t]b[t]. However,
I got 0 actually. To debug, when I set

b[t] c[t] a'[t] /. b_ a_'[t] -> b

I get b[t] c[t]. Thus pattern matching works and it appears D[b,t]
should be non-zero.

Any ideas how I can get D[b[t]c[t], t] in the above pattern
replacement? Thanks!