       Re: Derivative of a sum.

• To: mathgroup at smc.vnet.net
• Subject: [mg101632] Re: [mg101615] Derivative of a sum.
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 12 Jul 2009 05:48:35 -0400 (EDT)

```Presumably you meant the sum to be

f[x_, n_] = E^(-x)*Sum[x^i/i!, {i, 0, n}]

Gamma[n + 1, x]/n!

fp[x_, n_] = D[f[x, n], x]

-(x^n/(E^x*n!))

Manipulate[
Plot[{
Tooltip[f[x, n], "f"],
Tooltip[fp[x, n], "fp"]},
{x, 0, 5},
PlotRange -> {-1, 1}],
{n, 0, 4, Appearance -> "Labeled"}]

Bob Hanlon

---- Muntoni Giampaolo <muntoni.giampa at alice.it> wrote:

=============
In order to resolve a problem I have found the question of derivating  the
expression e^(-x)*Sum(in i)(x^n/n!, (i,0,n));the solution is easy and is
e^(-x)(x^n/n!).
But using language of Mathematica I have obteined a different result with a
ricorse of Gamma function...also recurring to the option of manipulate,
changing the value of  integer n.
I would want to obtain the exact result with language of Mathematica and
Manipulate respect to n and also plotting the original function and its
derivative.(with manipulate)
Thanks for aids
Giampaolo

```

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