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how to replace with definition

• To: mathgroup at smc.vnet.net
• Subject: [mg123669] how to replace with definition
• From: r_poetic <radford.schantz at mms.gov>
• Date: Thu, 15 Dec 2011 04:53:26 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello,
I can't seem to manage this replacement:

k[t] = A[t]/L[t];

L'[t] = lambda L[t]; A'[t] = s k[t]^alpha;

D[k[t],t]

output=  lambda A[t] + s (A[t]/L[t]) ^ alpha
              -----------------     -----------------------------
                     L[t]                    L[t]

How can the ratio A[t]/L[t] be replaced with k[t] here?  I have tried
a number of possibilities using /. or Replace.

• Follow-Ups:
  • Re: how to replace with definition
    • From: Bob Hanlon <hanlonr357@gmail.com>