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Re: Abs and derivative problems

• To: mathgroup at smc.vnet.net
• Subject: [mg14946] Re: Abs and derivative problems
• From: "Dale Horton" <daleh>
• Date: Fri, 27 Nov 1998 03:49:43 -0500
• Organization: Wolfram Research, Inc.
• References: <71q9qu$j25@smc.vnet.net> <728lbo$eit@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

The problem is that the FullForm of z'[t] does not contain z[t].

In[1]:=
FullForm[z'[t] + b z[t]]

Out[1]//FullForm=
Plus[Times[b,z[t]],Derivative[1][z][t]]

It does contain z, though. So you can replace z with the pure function
for t^2.

In[2]:=
z'[t] + b z[t]/.z->(#^2&)
Out[16]=
2 t + b t^2

-Dale

A.ODA wrote in message <728lbo$eit at smc.vnet.net>...

sylvan wrote in message <71q9qu$j25 at smc.vnet.net>...
>Also,  replacement rules like  //. z[t_] -> t^2 do not work well on
>expressions like  z'[t] + b z[t]. the result  is  z'[t] + b t^2... I
>could not force it to Evaluate z'[t] or D[z[t], t].
>
In this case, you can use "Hold" and "RelesseHold".

Define expression using "Hold" to postpone evalueation like derivatives.
After assign some rules, place "ReleaseHold" at the expression.

example

expr=D[Hold[z[t]],t]+b z[t]
(expr /. z[t]->t^2)//ReleaseHold

result in

2t + b t^2


A. ODA <a-oda at muj.biglobe.ne.jp>
Kawasaki, JAPAN