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MathGroup Archive 1998

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Re: Derivative via mathematica

> 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)


The definitions:

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

will do what You want

D[f[t,mu[t],beta[t]],t] //InputForm

   (1 + E^t^(-1) + beta[t]) - 
  (mu[t]*(-(E^t^(-1)/t^2) + 
   (1 + E^t^(-1) + beta[t])^2

> 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?

If You drop the definitions for Derivative[1][mu][_] and 
Derivative[1][beta][_] You get the mu'[t] amd beta'[t] output.

Hope that helps 

> Basically, it is a chain derivative question, I just want it to stop
> earlier.
> Could somebody help?
> Thanks.

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