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[ BUG ] REPORT: Distinct [ diff ], slanted [d] and Math differentiation [ Template ] operators Results for Differentiation with respect to [ More ] than 1 Variable
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I will be providing a Detailed [ BUG ] REPORT ( already described at the
http://www.tricider.com/brainstorming/2eKfifdjarx page ), which may have been still unnoticed at all ( due to the vast number of suggested items on that page ).
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The general syntax for [ Differentiation ] operator both by [ diff ] command or the slanted [d] symbol ( available from catalog ) is:
diff( expression, variable [, variable, [ ..., variable ] ] ] )
or
slanted [d]( expression, variable [, variable, [ ..., variable ] ] ] )
The results provided by [ Both ] forms of Differentiation should be the [ Same ], which unfortunately does [ Not ] happen for [ More ] than [ One ] variable ( even with Rev 8151 of the Kernel ), with only [ diff ] command producing the [ Correct ] result.
Take for example the Differentiation of x^2 * y^3 with respect to y and then to x by
diff( x^2 * y^3, y, x )
which Correctly produces 6*x*y^2
while by taking the Same compound Derivative by means of the slanted [d] symbol ( invoked from the command catalog )
[d]( x^2 * y^3, y, x )
Wrongly produces 0
If the Compound derivative were taken by Parts, even so the slanted [d] operator produces the Wrong result 0 by following the below order of instructions
First
[d]( x^2 * y^3, y ) correctly produces
3*x^2*y^2
if one now invokes the slanted [d] operator on the Produced last answer Result with respect to x one Correctly arrives at
[d]( 3*x^2*y^2, x )
resulting in 6*x*y^2
but if one applies a Chained slanted [d] operator, by means of
[d]( [d]( x^2*y^3, y ), x )
one arrives at the Wrong result of 0
Its interesting to Note that the slanted [d] Differentiation operator symbol, available from the [ Catalog ] of functions, presents a Differentiation [ Template ] at command line, while invoked, by the same way as invoking the differentiation Operator by touching on the Math Operations Template.
To make things a bit more Clear, from the Example provided, imagine one taking the following order of operations, by
First invoking Math Operations Template, then selecting the slanted [d] operator and entering the x^2 * y^3 expression at the numerator, and y variable at the denominator, producing the intermediate Differentiation only with respect to y
[d]( x^2 * y^3, y )
resulting in the Partial Result
3*x^2*y^2
if now one Invokes the Math Template again and selects the slanted [d] operator and uses the command [ History ], by means of the Upward motion ( of the four direction cursor ), and [ Selects ] the Previous entry [ Input ]
[d]( x^2 * y^3, y )
and press [ Enter ] as the Numerator expression to be now differentiated with respect to x variable ( at the Denominator ), one ends up with the [ Compound ] differentiation input first by y and then by x
[d]( [d]( x^2*y^3, y ), x )
which produces the Wrong result 0
If after invoking Math Template and selecting slanted [d] operator ( with respect to y variable ) instead of [ Selecting ] the Previous entry [ Input ] " [d]( x^2 * y^3, y ) " ( by means of the Upward cursor ) one [ Selects ] the previous entry [ Output ] " 3*x^2*y^2 " as the Numerator, and specifies the x variable at the Denominator, one Correctly arrives at
[d]( 3*x^2*y^2, x )
producing the Right answer 6*x*y^2
Its also interesting to note that while filling the Differentiation [ Template ] one may specify [ Compound ] Derivatives, by simply providing the [ List ] of Variables, separated by [ , ] Comma, at the [ Denominator ] of the Template.
So one may Select the slanted [d] operator from Math Template, and provide the desired expression like x^2 * y^3 at the Numerator and provide " y,x " as the Denominator Variables [ List ], which will effectively produce
[d]( [d]( x^2*y^3, y ), x )
which unfortunately produces the [ Wrong ] result of 0
Other Examples of [ Compound ] Differentiation just for Reference ( and to complement the provided example ), allowing for a Better compreension of What may be Actually going [ Wrong ] with [ Compound ] Variable Differentiation with the slanted [d] operator on Kernel 8151 of HP Prime are
[d]( [d]( [d]( x^n, x ), x ), x )
which produces the [ Right ] answer
while
[d]( x^n, x, x, x )
by providing the x,x,x [ List ] at the [ Denominator ] of the differentiation [ Template ]
produces the [ Wrong ] answer
n*x^(-1+n)
Its also interesting to note that
diff( x^n, x, x, x )
or
diff( x^n, x$3 )
produces the [ Right ] answer.
Its Clear that Distinct [ Compound ] Differentiation [ options ] provided by HP Prime by means of the [ diff ] operator command and the slanted [d] operator symbol ( from catalog ) and the Math Operations Template should be [ REVISED ] since undesirable Wrong results are Produced by Compounding the slanted [d] operator.
It seems that some sort of [ Distinct ] Operator [ Priority ] for the [ diff ] command and slanted [d] symbol may be causing such problems.
Yours Sincerely, with my Best Wishes to All,
Prof. Ricardo Duarte
![[Image: 2015-08-09_1340.png]](http://content.screencast.com/users/erwinried/folders/Jing/media/40bbcaee-41d9-4a13-b63e-6ec11a498a28/2015-08-09_1340.png)
![[Image: 2015-08-09_1344.png]](http://content.screencast.com/users/erwinried/folders/Jing/media/ca5a5a7e-28f7-4c92-bf51-3f5db3045e45/2015-08-09_1344.png)
(1123 visits)
It's "interesting" if it's something one has (relatively) recently been exposed to. But if you've depended on it all through college and your working life thereafter, it's something else entirely.![[Image: 11.10.2017-13.09.png]](https://content.screencast.com/users/erwinried/folders/Snagit/media/68e90036-26c3-4a42-b2d0-6495543ae834/11.10.2017-13.09.png)
![[Image: 11.10.2017-13.22.png]](https://content.screencast.com/users/erwinried/folders/Snagit/media/2a179a8a-bf2e-461f-911f-244f8eec5e54/11.10.2017-13.22.png)
![[Image: 11.10.2017-13.32.png]](https://content.screencast.com/users/erwinried/folders/Snagit/media/18eea514-1a5f-43dd-9430-2061f3b3026b/11.10.2017-13.32.png)