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Weird answer for d(sin(sin(x)))/dx - Printable Version

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Weird answer for d(sin(sin(x)))/dx - ettlz - 07-29-2018 01:11 PM

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.

RE: Weird answer for d(sin(sin(x)))/dx - Tim Wessman - 07-29-2018 01:13 PM

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.

RE: Weird answer for d(sin(sin(x)))/dx - ettlz - 07-29-2018 01:18 PM

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!)

RE: Weird answer for d(sin(sin(x)))/dx - parisse - 07-29-2018 01:38 PM

It's not "more complicated", it's different, the product of cosines has been replaced by a sum.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.

RE: Weird answer for d(sin(sin(x)))/dx - Aries - 07-29-2018 02:21 PM

(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

RE: Weird answer for d(sin(sin(x)))/dx - Tim Wessman - 07-29-2018 03:57 PM

Yes, which is exactly what Prime gives in it's default state. Smile

RE: Weird answer for d(sin(sin(x)))/dx - Komanguy - 07-29-2018 04:06 PM

(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

RE: Weird answer for d(sin(sin(x)))/dx - Komanguy - 07-29-2018 04:12 PM

(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!

RE: Weird answer for d(sin(sin(x)))/dx - DrD - 07-29-2018 04:19 PM

(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!

RE: Weird answer for d(sin(sin(x)))/dx - Komanguy - 07-29-2018 04:25 PM

(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.

RE: Weird answer for d(sin(sin(x)))/dx - DrD - 07-29-2018 05:43 PM

Results from the various Simplify options:
{Maximum, Minimum, None}
[attachment=6167]