HP50g derivatives

04022017, 07:03 PM
Post: #1




HP50g derivatives
I've encountered he following "glitch" with the HP50g:
Storing S^2 in variable T, the command DS(sin(T)) will expand to DS(sin(T)) = DS(sin(S^2) = 2Scos(S^2), which is just fine. Storing S^2 in in variable T as above, according to Nick K's "Calculus Marathon on the HP49G" the command DT(sin(T)) should expand to DT(sin(T)) = cos(T=S^2) = cos(s^2). But it doesn't! Instead, the result is DT(sin(T)) = 0, which suggests that the expansion rule in this case reads: DT(sin(T)) = DT(sin(S^2)) = 0. That's bad ... I'm wondering if there is a difference known in the defininition of D (derivative) in the 49g Firmware and the 50g Firmware (Rom version 2.15) or if I'm just missing something here? 

04032017, 04:45 AM
(This post was last modified: 04032017 04:48 AM by Carsen.)
Post: #2




RE: HP50g derivatives
Hi there! I will try to attempt to help you here.
I got the correct answer by doing the following keystrokes in RPN mode... [ALPHA] S [LS] [X^2] [ ' ] [ALPHA] T [STO>] [ ' ] [ALPHA] T [ENTER] [ENTER] SIN [Right Arrow] [RS] [ ∂ ] < (Orange function above the COS key) [RS] [ALG] [EXPAN] < (F2 key) Which gives me COS(S^2) If you wish to do this in ALG mode, do this... [LS] [X^2] [ALPHA] S [Right Arrow] [STO>] [ALPHA] [T] [ENTER] [RS] [ALG] [EXPAN]>(F2 Key) [RS] [ ∂ ] [ALPHA] T [LS] [ () ] SIN [ALPHA] T [ENTER] [RS] = The orange shift key, [LS] = The white shift key, [ ' ] = The Tick key In ALG mode, it's essentially the derivative function using the HP 50g's keyboard is inside the Expand function. In RPN mode, just make sure to use the Tick key to make sure the T does not turn into S^2. I get COS(S^2) as a result for both methods. Let me know if there are any questions or confusion on my keystroke examples above. I used the HP 50g 2.15 version so it should work. 

04032017, 07:18 PM
Post: #3




RE: HP50g derivatives
(04032017 04:45 AM)Carsen Wrote: Hi there! I will try to attempt to help you here. Hi Carsen! The methods you are suggesting do give the expected results, thank you very much for this!! But still, I do not understand why [ALPHA] S [LS] [X^2] [ ' ] [ALPHA] T [STO>] [ ' ] [ALPHA] T [ENTER] [ENTER] [ ' ][RS] [ ∂ ] [ALPHA] T [LS] [ () ] SIN [ALPHA] T [ENTER] [RS] [ALG] [EXPAN] does not do the job but expands to 0 (Zero). The only difference (as far as I can figure) is that I used RPN to store S^2 in T and called the derivative on the stack in ALG Fashion, that is by '∂T(sin(T))' [ENTER] [EXPAN]. Shouldn't that give the desired result also? 

04042017, 03:41 AM
Post: #4




RE: HP50g derivatives
Make sure that in RPN mode, put the variable T onto the stack by pressing the [ ' ] key first and then [ALPHA] [T] [ENTER]. This is the key to this entire problem because it puts the letter T onto the stack without turning into the S^2. Now you can press the [SIN] key and it should say SIN(T) on level 1. Then, put the variable T on the stack again with the same process, press the [ ' ] key and then press [ALPHA] [T] [ENTER]. Now all you need to do is execute DERIV or ∂ function above the [COS] key to derive the function, which gives you COS(T). Then use the EXPAN function to transform the answer COS(T) into COS(S^2).
For ALG mode, I have tried to attached a picture that has the steps I used to get my answer but I couldn't. It said that my file was too big. So I will have to explain it with words again. Notice how the EXPAN function is around the derivative so that it looks like this BEFORE pressing enter... EXPAND(∂T(SIN(T))
That's the key to getting this to work. I have tried doing the exact same command without the EXPAND function around the derivative but it did not work. I got the answer 0. You  for some odd reason  NEED the derivative function inside the EXPAND function. You also need to use the derivative function that is on the [COS] key when using ALG mode. It's the shifted orange function that looks like this... ∂
Are you doing that? Do you know how? I have tried to use the DERIV function inside the expand function but it does not work. You need to also use the derivative function that is shifted on the [COS] key. Any confusion? Any more questions? Please ask! I am definitely not an expert of this machine so explaining why the derivative needs to be inside the expand function is beyond my knowledge. I had the same problem with my limit problems except it said "Error: Non algebraic in expression".So I figured out that I needed to have my limit inside the EXPAN function in order to get an answer and it worked. I have only owned this machine for about 6 months now. Although, my guess is that ALG mode is somewhat incomplete and that's why the EXPAN function is needed. I don't really know though. Anyway, I hope this gets you the explanation you need. 

04042017, 07:33 PM
Post: #5




RE: HP50g derivatives
Hi Carsen, thanks again for your comprehensive description!
Quote:Are you doing that? Do you know how? ... Any confusion? Any more questions?Yes, Carsen, I'm doing that, I'm using the derivative function triggered by ∂. And the procedures suggested by you, both in RPN and in ALG mode, work for me just fine as well. Furthermore, I do understand the logic behind the procedures (especially the reason why the variabel has to be equipped wit tick marks before putting it on the stackof)  even though to have the EXPANfunction wrapped around the derivative to make it work is odd  and exactly that is what I do not understand from an Logical Point of view: 'T' S^2 STO '∂T(sin(T))' ENTER EXPAN should  RPNLogic wise  be the same as 'T' S^2 STO 'EXPAN(∂T(sin(T)))' ENTER  but it isn't. For me this is an inconsitency in the derivative function. Anyway, thank you very much again for figuring out this "glitch" and showing ways how to circumnavigate this :) 

04042017, 08:42 PM
Post: #6




RE: HP50g derivatives
I'm just happy to help, JurgenRo! This calculator is quirky and picky at times and this calculator has had me frustrated a lot.
But at the top of the HP 50g mountain, it's a beautiful view. 

04042017, 09:26 PM
Post: #7




RE: HP50g derivatives
(04042017 08:42 PM)Carsen Wrote: I'm just happy to help, JurgenRo! This calculator is quirky and picky at times and this calculator has had me frustrated a lot. Hi Carsen, I know what you mean ;) That's why I love to do the 49gMarathons by Nick Karagiaouroglou. What beautiful documents to really Grandmaster the hp50g! If you don't know them, just have a look here and search for "Nick"  you won't regret it: http://www.hpcalc.org/hp49/docs/misc/ 

04062017, 08:32 PM
Post: #8




RE: HP50g derivatives
NEAT! This is actually pretty cool! Instead of ciphering through the HP Manuals and experimenting for the answer. I can go through these marathons and slowly master the HP 50g a bit more. How did I not find this?
And with these tools, a Grandmaster of the HP 50g I shall become! Thanks a bunch! 

04072017, 11:19 PM
Post: #9




RE: HP50g derivatives
I do admire these works a lot  great you like too!


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