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]