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MathGroup Archive 1998

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Re: Derivative via mathematica


  • To: mathgroup@smc.vnet.net
  • Subject: [mg10533] Re: [mg10486] Derivative via mathematica
  • From: Bob Hanlon <BobHanlon@aol.com>
  • Date: Tue, 20 Jan 1998 02:23:19 -0500
  • Organization: AOL (http://www.aol.com)

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

m/: Dt[m, t] = p;
b/: Dt[b, t] = q;

D[f[t, m[t], b[t]], t]

\!\(\*
  RowBox[{
    RowBox[{"-", 
      FractionBox[
        RowBox[{\(m[t]\), " ", 
          RowBox[{"(", 
            RowBox[{\(-\(E\^\(1\/t\)\/t\^2\)\), "+", 
              RowBox[{
                SuperscriptBox["b", "\[Prime]",
                  MultilineFunction->None], "[", "t", "]"}]}], ")"}]}], 
        \(\((1 + E\^\(1\/t\) + b[t])\)\^2\)]}], "+", 
    FractionBox[
      RowBox[{
        SuperscriptBox["m", "\[Prime]",
          MultilineFunction->None], "[", "t", "]"}], 
      \(1 + E\^\(1\/t\) + b[t]\)]}]\)

Dt[f[t, m, b], t]

\!\(p\/\(1 + b + E\^\(1\/t\)\) - 
    \(m\ \((q - E\^\(1\/t\)\/t\^2)\)\)\/\((1 + b + E\^\(1\/t\))\)\^2\)


Bob Hanlon



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