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Derivative via mathematica

• To: mathgroup@smc.vnet.net
• Subject: [mg10486] Derivative via mathematica
• From: cai <cai@iris7.cici.ohiou.edu>
• Date: Fri, 16 Jan 1998 04:35:09 -0500
• Organization: Ohio University

Hi,

I just used mathematica for a couple of days.  I am trying to compute
the derivative under mathematica.  Because the function is complicated,
I like to break it down.

f[t_] = (m/(1+Exp[1/t] +b)

Here m and b are functions of t.
If I directly use command D after insert m and b terms, a very
complicated equaion is gerenated, which I do not want.

What I want is if I define the values of m' and b', rewrite the f

m' = p
b' = q   // well, I dont know how to define, this is the idea

f[t_, m[t], b[t]] = (m/(1+Exp[1/t] +b)

then use the command D[f[t,m[t],b[t]],t] hopeful get a equation which is
the function of t, p and q.  How to do that?

A related question, I tried to use non-defined function In[19]:= m[t_]
Out[19]= m[t_]
In[20]:= D[m[t],t]
Out[20]= m'[t]
and expected D[f[t,m[t],b[t]],t] contains m'[t].  Is it possible?

Basically, it is a chain derivative question, I just want it to stop
earlier.

Could somebody help?
Thanks.

ccai1@ohiou.edu