Re: Derivative
- To: mathgroup at smc.vnet.net
- Subject: [mg43724] Re: Derivative
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 2 Oct 2003 02:51:18 -0400 (EDT)
- Organization: The University of Western Australia
- References: <blcqiv$p7d$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <blcqiv$p7d$1 at smc.vnet.net>, "extrabyte" <extrabyte22 at libero.it> wrote: > I have these functions (see http://mynotebook.supereva.it) > > g[x_,y_]:=(Exp[x-y]+1)^-1; > > theta[x_,y_]:=ArcCosh[x*y]; > > F[y_]:=NIntegrate[g[x,y]*Sinh[theta[x,y]]*(Cosh[theta[x,y]])^2,{x,y,+oo},Wor > kingPrecision->15, AccuracyGoal->20, MinRecursion->3, MaxRecursion->10] > > I must now calculate: > > f[y_]:=Evaluate[D[F[y]],y] > > but Mathematica running.......... First use the fundamental theorem of calculus: for an arbitrary function h[x,y], we have D[Integrate[h[x,y],{x,y,Infinity}],y] == Integrate[Derivative[0, 1][h][x, y], {x, y, Infinity}] - h[y, y] Now define h, h[x_, y_] = Simplify[g[x, y] Sinh[theta[x, y]] Cosh[theta[x, y]]^2]; and compute its derivative with respect to y. dhdy[x_, y_] = Simplify[D[h[x,y],y]]; Now we can define f: f[y_] := NIntegrate[dhdy[x, y], {x, y, Infinity}, WorkingPrecision -> 15, AccuracyGoal -> 20, MinRecursion -> 3, MaxRecursion -> 10] - h[y, y] Cheers, Paul -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul