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Weird answer for d(sin(sin(x)))/dx
07-29-2018, 01:11 PM
Post: #1
Weird answer for d(sin(sin(x)))/dx
Prime 2.0.0.13865 gives a bizarre form of the derivative of sin(sin(x)): I get (1/2)*cos(sin(x)+x) + (1/2)*cos(-sin(x)+x). OK it's correct but I'd expect cos(sin(x))*cos(x) (straightforward chain rule). Getting to that form doesn't work with simplify() and I've not played around with the other trig-rewrite functions.
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07-29-2018, 01:13 PM (This post was last modified: 07-29-2018 01:16 PM by Tim Wessman.)
Post: #2
RE: Weird answer for d(sin(sin(x)))/dx
I am guessing you have simplified to "maximum"? "Maximum" is equivalent to just tapping the "simplify" button on each result.

I'd highly recommend not doing that if you are and leave the default "minimum" - it has a tendency to mess things up and we will probably remove that option completely at some point before too much longer.

TW

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07-29-2018, 01:18 PM (This post was last modified: 07-29-2018 01:25 PM by ettlz.)
Post: #3
RE: Weird answer for d(sin(sin(x)))/dx
Ah yes. It seems cos(x)*cos(sin(x)) is one of those cases where simplify() makes things more complicated.

Going the other way, the HP 50g's SIMPLIFY does get from the long form back to cos(x)*sin(cos(x)), so there's a sort-of "regression" here. (Well, assuming the Prime represents a functional continuation... which probably isn't entirely fair!)
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07-29-2018, 01:38 PM
Post: #4
RE: Weird answer for d(sin(sin(x)))/dx
It's not "more complicated", it's different, the product of cosines has been replaced by a sum. There is no way to magically "simplify" because there is no simpler form.
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07-29-2018, 02:21 PM
Post: #5
RE: Weird answer for d(sin(sin(x)))/dx
(07-29-2018 01:11 PM)ettlz Wrote:  Prime 2.0.0.13865 gives a bizarre form of the derivative of sin(sin(x)): I get (1/2)*cos(sin(x)+x) + (1/2)*cos(-sin(x)+x). OK it's correct but I'd expect cos(sin(x))*cos(x) (straightforward chain rule). Getting to that form doesn't work with simplify() and I've not played around with the other trig-rewrite functions.

[Image: dertrig.jpg]immagini su internet

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Aries Wink
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07-29-2018, 03:57 PM
Post: #6
RE: Weird answer for d(sin(sin(x)))/dx
Yes, which is exactly what Prime gives in it's default state. Smile

TW

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07-29-2018, 04:06 PM
Post: #7
RE: Weird answer for d(sin(sin(x)))/dx
(07-29-2018 02:21 PM)Aries Wrote:  
(07-29-2018 01:11 PM)ettlz Wrote:  Prime 2.0.0.13865 gives a bizarre form of the derivative of sin(sin(x)): I get (1/2)*cos(sin(x)+x) + (1/2)*cos(-sin(x)+x). OK it's correct but I'd expect cos(sin(x))*cos(x) (straightforward chain rule). Getting to that form doesn't work with simplify() and I've not played around with the other trig-rewrite functions.

[Image: dertrig.jpg]immagini su internet

Best,

Aries Wink


Hp prime gives the same result. Smile

Guy R. KOMAN, hp 50G, hp Prime Rev. C
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07-29-2018, 04:12 PM (This post was last modified: 07-29-2018 04:23 PM by Komanguy.)
Post: #8
RE: Weird answer for d(sin(sin(x)))/dx
(07-29-2018 03:57 PM)Tim Wessman Wrote:  Yes, which is exactly what Prime gives in it's default state. Smile


diff(sin(sin(x))) always gives : cos(x)*cos(sin(x)) independently of the simplification mode in cas settings!


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07-29-2018, 04:19 PM
Post: #9
RE: Weird answer for d(sin(sin(x)))/dx
(07-29-2018 04:12 PM)Komanguy Wrote:  diff(sin(sin(x))) always gives : cos(x)*cos(sin(x)) independently of the simplification mode in cas settings!

Now try it on the physical prime!
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07-29-2018, 04:25 PM
Post: #10
RE: Weird answer for d(sin(sin(x)))/dx
(07-29-2018 04:19 PM)DrD Wrote:  
(07-29-2018 04:12 PM)Komanguy Wrote:  diff(sin(sin(x))) always gives : cos(x)*cos(sin(x)) independently of the simplification mode in cas settings!

Now try it on the physical prime!

I have the physical one. I don’t use the emulator.


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07-29-2018, 05:43 PM (This post was last modified: 07-29-2018 05:45 PM by DrD.)
Post: #11
RE: Weird answer for d(sin(sin(x)))/dx
Results from the various Simplify options:
{Maximum, Minimum, None}
[attachment=6167]
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