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From: Merciadri Luca on 8 Dec 2009 10:21
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Hi,

Let's say I want to evaluate
\[
\frac{\partial f^5}{\partial x^2 \partial y^3}f(x,y),
\]
for a sufficiently differentiable f(x,y), with my HP 50g. I can do it
manually, /i.e/ using the \partial command, but it becomes tedious
when one needs to evaluate some higher than 2 or three derivatives. Is
there a way to ask it to do, for example, \partial y^3? In reality,
one writes it, but I do not know how to ask the calculator to do it,
except by a mere manual way.

Thanks for any answer.

- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
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From: rs1n on 8 Dec 2009 10:55
Input:
2: list of variables
1: function

In the program below, the "d" stands for the derivative command.

store the program below as PARTIAL:
<<
OVER SIZE 1 SWAP
FOR n
OVER n GET d
NEXT
SWAP DROP
>>

Example: Compute the mixed second partial of f(x,y) = x^2 * y + e^(y
* x)

2: { X Y }
1: 'X^2*Y + EXP(Y*X)

PARTIAL

returns:

'2*X + (EXP(Y*X) + (X* EXP(Y*X)))'


On Dec 8, 10:21 am, Merciadri Luca <Luca.Mercia...(a)student.ulg.ac.be>
wrote:
> -----BEGIN PGP SIGNED MESSAGE-----
> Hash: SHA1
>
> Hi,
>
> Let's say I want to evaluate
> \[
> \frac{\partial f^5}{\partial x^2 \partial y^3}f(x,y),
> \]
> for a sufficiently differentiable f(x,y), with my HP 50g. I can do it
> manually, /i.e/ using the \partial command, but it becomes tedious
> when one needs to evaluate some higher than 2 or three derivatives. Is
> there a way to ask it to do, for example, \partial y^3? In reality,
> one writes it, but I do not know how to ask the calculator to do it,
> except by a mere manual way.
>
> Thanks for any answer.
>
> - --
> Merciadri Luca
> Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/
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>
> iEYEARECAAYFAksebuAACgkQM0LLzLt8Mhzi5wCggA3ZLSJrW0kGuZ32yZWTkajx
> /eYAoJtEBpgPnmt+FKhZE3vZRAK/nhGf
> =OJLl
> -----END PGP SIGNATURE-----

From: Merciadri Luca on 8 Dec 2009 15:17
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Hash: SHA1

rs1n <handuongster(a)gmail.com> writes:

> Input:
> 2: list of variables
> 1: function
>
> In the program below, the "d" stands for the derivative command.
>
> store the program below as PARTIAL:
> <<
> OVER SIZE 1 SWAP
> FOR n
> OVER n GET d
> NEXT
> SWAP DROP
>>>
>
> Example: Compute the mixed second partial of f(x,y) = x^2 * y + e^(y
> * x)
>
> 2: { X Y }
> 1: 'X^2*Y + EXP(Y*X)
>
> PARTIAL
>
> returns:
>
> '2*X + (EXP(Y*X) + (X* EXP(Y*X)))'
Thanks for this answer. Nice, but how to compute only a *partial* one to
a given order?

- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
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From: rs1n on 8 Dec 2009 15:45
Just use the same program. For example:

\[ \frac{\partial^3 f}{\partial y^3} f(x,y) \]

Using the same example as before, put on the stack:

2: { Y Y Y }
1: '2*X^2*Y+EXP(Y*X)'

and run the program. This will give you the desired third partial
derivative with respect to y. If the list on level 2 contains n
variables, then you are computing the n-th partial, with respect to
whichever variable is in the list (left-most variable first; of
course, the order does not matter since the variables are linearly
independent)


> Thanks for this answer. Nice, but how to compute only a *partial* one to
> a given order?
>
> - --
> Merciadri Luca
> Seehttp://www.student.montefiore.ulg.ac.be/~merciadri/
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> iEYEARECAAYFAksetGwACgkQM0LLzLt8MhxdbgCffBGpERqN/tjAR4WtRHOeiMGg
> YxYAnAwOr0csiNodppE9hmzwnWo7dhjg
> =bLx3
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> - Show quoted text -

From: Merciadri Luca on 9 Dec 2009 10:31
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Hash: SHA1

rs1n <handuongster(a)gmail.com> writes:

> Just use the same program. For example:
>
> \[ \frac{\partial^3 f}{\partial y^3} f(x,y) \]
>
> Using the same example as before, put on the stack:
>
> 2: { Y Y Y }
> 1: '2*X^2*Y+EXP(Y*X)'
>
> and run the program. This will give you the desired third partial
> derivative with respect to y. If the list on level 2 contains n
> variables, then you are computing the n-th partial, with respect to
> whichever variable is in the list (left-most variable first; of
> course, the order does not matter since the variables are linearly
> independent)
Thanks. I had not realized that it could have been used like this
too.

- --
Merciadri Luca
See http://www.student.montefiore.ulg.ac.be/~merciadri/
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