Confusing derivative(sqrt(1-sinx)) result Bug? [SOLVED]
05-04-2018, 09:12 PM (This post was last modified: 05-27-2018 12:28 PM by vvolkan.)
Post: #1
 vvolkan Junior Member Posts: 15 Joined: Apr 2018
Confusing derivative(sqrt(1-sinx)) result Bug? [SOLVED]
Derivative of sqrt(1-sinx) should be -cosx/2sqrt(1-sinx) but it returns a long confusing result and it cant be simplified.
05-05-2018, 07:48 AM
Post: #2
 Arno K Senior Member Posts: 432 Joined: Mar 2015
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
As I get everything correct in CAS on the emulator you should show us a screenshot.
Arno
05-05-2018, 09:24 AM (This post was last modified: 05-05-2018 01:46 PM by vvolkan.)
Post: #3
 vvolkan Junior Member Posts: 15 Joined: Apr 2018
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
Hi Arno,
I tried on HP Prime Pro app and pc(both rev.13441),same result. Here are the screenshots from pc.
Volkan

Attached File(s) Thumbnail(s)

05-05-2018, 10:15 AM (This post was last modified: 05-05-2018 10:20 AM by DrD.)
Post: #4
 DrD Senior Member Posts: 1,117 Joined: Feb 2014
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
(05-04-2018 09:12 PM)vvolkan Wrote:  Derivative of sqrt(1-sinx) should be cosx/2sqrt(1-sinx) but it returns a long confusing result and it cant be simplified.

[emulator]:
The result should include a negative sign: (-1/2)*cos(x)*1/(sqrt(1-sin(x))).
[attachment=5888] [attachment=5889]
05-05-2018, 10:45 AM
Post: #5
 Aries Member Posts: 148 Joined: Oct 2014
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
(05-04-2018 09:12 PM)vvolkan Wrote:  Derivative of sqrt(1-sinx) should be cosx/2sqrt(1-sinx) but it returns a long confusing result and it cant be simplified.

Best,

Aries
05-05-2018, 12:43 PM (This post was last modified: 05-05-2018 12:47 PM by parisse.)
Post: #6
 parisse Senior Member Posts: 1,090 Joined: Dec 2013
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
sqrt(1-sin(x)) is auto-simplified to sqrt(2)*abs(sin(-pi/4+x/2)), because it's much better not to deal with "false" sqrt, for example if you want to integrate sqrt(1-sin(x)).
The derivative is sqrt(2)*cos(x/2-pi/4)*abs(sin(x/2-pi/4))/(2*sin(x/2-pi/4)), it looks complicated but it is not: it's the product of a cos by a sign. If you make assumptions on x like
assume(x>0 && x<pi/2), you will not get absolute values, and the derivative is simpler -sqrt(2)*cos(x/2-pi/4)/2
05-05-2018, 01:43 PM (This post was last modified: 05-05-2018 03:33 PM by vvolkan.)
Post: #7
 vvolkan Junior Member Posts: 15 Joined: Apr 2018
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
It seems as calc gives different variation of result if "√" is used instead of "^1/2" for this derivative. Thanks parisse for comprehensive explanation.

Attached File(s) Thumbnail(s)

05-05-2018, 07:24 PM (This post was last modified: 05-05-2018 10:57 PM by vvolkan.)
Post: #8
 vvolkan Junior Member Posts: 15 Joined: Apr 2018
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
(05-05-2018 10:15 AM)DrD Wrote:
(05-04-2018 09:12 PM)vvolkan Wrote:  Derivative of sqrt(1-sinx) should be cosx/2sqrt(1-sinx) but it returns a long confusing result and it cant be simplified.

[emulator]:
The result should include a negative sign: (-1/2)*cos(x)*1/(sqrt(1-sin(x))).

Hi DRD,
I forgot to write the negative sign. I edited the main post. I shared screenshots to clarify the problem. Thanks
05-05-2018, 09:15 PM
Post: #9
 Arno K Senior Member Posts: 432 Joined: Mar 2015
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
(05-05-2018 01:43 PM)vvolkan Wrote:  It seems as calc gives different variation of result if "√" is used instead of "^1/2" for this derivative. Thanks parisse for comprehensive explanation.

Arno
05-06-2018, 06:40 AM
Post: #10
 parisse Senior Member Posts: 1,090 Joined: Dec 2013
RE: Wrong derivative(sqrt(1-sinx)) result Bug?
Another way to get it: sqrt(a-sin(x))'
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