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MathGroup Archive 2005

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Mathematica takes wrong derivative

  • To: mathgroup at smc.vnet.net
  • Subject: [mg59650] Mathematica takes wrong derivative
  • From: "Mukhtar Bekkali" <mbekkali at gmail.com>
  • Date: Tue, 16 Aug 2005 04:39:31 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

I believe Mathematica 5.0.1.0 takes wrong derivative. See my code below
where I plotted the function D2 and its derivative. The derivative is
obviously wrong.

[quote]

\!\(\(Clear["\<Global`*\>"];\)\[IndentingNewLine]
  {r, u, λ, Ï?, γ} = {2, 4, \(9\/10\) u\/\(1 + u\), 1 - \(λ\/\(1 -
λ\)\) 1\/u, \
\((1 - β)\)\^r\/\(\(β\^β\) \((1 - β)\)\^\(1 -
β\)\)}\[IndentingNewLine]
  \(z1 = \((\(β\^β\) \(\((1 - β)\)\^\(1 -
            β\)\) γ \((\(\(\ \)\(u\)\)\/\(1 + u\))\))\)\^\(-1\);\)\
\[IndentingNewLine]
  \(z2 = \((\(δ\^β\) \(\((1 - δ)\)\^\(1 - β\)\) γ \((\(u \((1 -
β)\)\)\/\(u \
\((1 - β)\) + 1\))\)\^\(1 - β\))\)\^\(-1\);\)\[IndentingNewLine]
  V21 := NIntegrate[z2\^\(-u\), {β, 0, \(δ \((1 + u)\)\)\/u}]\
\[IndentingNewLine]
  V22 := NIntegrate[z1\^\(-u\), {β, \(δ \((1 + u)\)\)\/u, 1}]\
\[IndentingNewLine]
  D2[δ_?NumericQ] := \((δ\
      V21 + NIntegrate[\(\(β\ u\)\/\(1 + u\)\) z1\^\(-u\), {β, \(δ
\((1 + \
u)\)\)\/u, 1}])\) \((V21 + V22)\)\^\(-Ï?\)\[IndentingNewLine]
  \(Plot[Evaluate[D2[δ]], {δ, 0, u\/\(1 + u\)}];\)\[IndentingNewLine]
  \(Plot[Evaluate[D[D2[δ], δ]], {δ, 0, u\/\(1 + u\)}];\)\)

[/quote]


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