Re: Derivatives D[ ] as Functions inside Tables; Need Help!

• To: mathgroup at smc.vnet.net
• Subject: [mg13203] Re: Derivatives D[ ] as Functions inside Tables; Need Help!
• From: "Allan Hayes" <hay at haystack.demon.cc.uk>
• Date: Mon, 13 Jul 1998 07:42:52 -0400
• References: <6nsil0\$f32@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```AES wrote in message <6nsil0\$f32 at smc.vnet.net>...
>I'm trying to define a function f1[a,x] and its derivative f2[a,x],
>where from my point of view x is the independent variable and   "a" is
>a parameter I'll change on different runs.  So I write, as a simple
>example:
>
>   Remove["Global`*"]
>
>   f1[a_,x_] :=a Cos[x] + a^2 Sin[x]
>
>   f1[a,x]
>
>   f2[a_,x_] := D[f1[a,x],x]
>
>   f2[a,x]
>
>   a=2
>
>   f1[a,x]
>
>   f2[a,x]
>
>   Table[{x, f1[a,x], f2[a.x]} // N, {x,0,4}] // TableForm
>
>and everything looks fine -- except the function f2[a,x] will not
>evaluate inside the Table[ ].  I don't understand this -- help in
>understanding will be much appreciated.
>
>     siegman at ee.stanford.edu

>

Clear["Global`*"]

f1[a_,x_] :=a Cos[x] + a^2 Sin[x];
f2[a_,x_] := D[f1[a,x],x];

The main problem is that Table finds the f2[x,y] for x = 1, say, by a
process like

x=1;
f2[a,x]
General::ivar: 1 is not a valid variable.
2
D[a Cos[1] + a  Sin[1], 1]

We need to evaluate the symbolic f2[a,x] before x takes the value 1

x=1;
Block[{x},f2[a,x]]

2
a  Cos[1] - a Sin[1]

With the example given, the pre-evaluation can be achieved in several
ways:

a=2;

(1)

Table[Block[{x},{x, f1[a,x], f2[a,x]}]//N , {x,0,4}] // TableForm

0    2.        4.

1.   4.44649   0.478267

2.   2.8049    -3.48318

3.   -1.4155   -4.24221

4.   -4.3345   -1.10097

(2)
x=. (* essential*)

Table[Evaluate[{x, f1[a,x], f2[a,x]}] , {x,0,4}]//N // TableForm

0    2.        4.

1.   4.44649   0.478267

2.   2.8049    -3.48318

3.   -1.4155   -4.24221

4.   -4.3345   -1.10097

(3)

Make the definitions of f1 and f2 immediate, so that the differention is
done before we construct the Table expression - this is the most
efficient way.

Clear["Global`*"]

f1[a_,x_] =a Cos[x] + a^2 Sin[x];
f2[a_,x_] = D[f1[a,x],x];

a=2;

Table[{x, f1[a,x], f2[a,x]} // N, {x,0,4}] // TableForm

0    2.        4.

1.   4.44649   0.478267

2.   2.8049    -3.48318

3.   -1.4155   -4.24221

4.   -4.3345   -1.10097

------------------------------------------------------------- Allan
Hayes
Training and Consulting
Leicester UK
http://www.haystack.demon.co.uk
hay at haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44(0)116 271 8642

```

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