Finding Power Series by Differentiation - 3 examples

[@BloodlessSalvation]

When you apologize for a long video, you realize this 13 minute video helped me more than reading and staring at the textbook for 2 hours and trying to figure out why I have to multiply by a half to the series on part b.

[@marcusj.merritt6862]

I admittedly do the same thing with my calc book everyday as well. [facepalm]

[@zuhrymousa12345]

KimichiSushi 100% true!

[@ExecrationZero]

+KimichiSushi People learn differently.

[@Nixiliog]

can't be anymore truer. Why do textbooks have to be written like darn hieroglyphics T_T

[@brucelee570]

I think you've helped raise the collective gpa of calculus students more than the infinite sum of 1/n

[@lorib285]

GAACK!!! This stuff takes some intuition I just don't have yet! Keep this up please so I'll have a prayer!

[@mollydenton6724]

Was panicking all day because I have a quiz over this tomorrow and havent been able to figure it out. You truly rock my dude

[@jjrimz99tandem_drifter]

in the 12 minutes i have watched this video, it took my teacher 2 hours. Mad props!

[@dhbballer16]

Wow I could not for the life of me understand how to differentiate a function when given a known series... This was a life saver! Thanks so much:)

[@2ttaher253]

I`m student in ksa in FBSU Your lessons and Your style of the callouts lessons very useful and wonderful I benefited from your lessons of two years thank you so much keep going

[@anamattson4442]

I have been confused for weeks, happened upon this video, and now get it! Thank you much.

[@Katie75522]

U r my savior, Patrick. If I ever see you one day on the street, expect a high-five 4-sure

[@vivaldikonzsmith7291]

He actually expects a little appreciation with some dollars, I am pretty sure your high five dont pay bills.

[@IIOXIDIZEII]

VERY helpful pat, 8:03 made me giggle. LOVE all your tricks and "what if" situations, they are thoroughly explained which help understand EVERYTHING!

[@allisonm4998]

You're my favorite.

[@patrickjmt]

+Allison M thanks!

[@bobbytrap2554]

I love how this is the exact example I was stuck on, thanks!

[@congcongai8081]

Your video explained everything well better than my college calculus teacher did.

[@fcortesjp]

on c) if i leave the index equal to 0 and not compensate for the shifting shouldnt that be ok since you are still getting 0's for first two values in the series when n=1 and n=0 ?

[@Mary-mj7le]

well i guess we'll never know

[@CarsonJamesCook]

I agree, for whatever that's worth (6 years later...).

[@aimaladil6564]

Assalam o Alaikum....patrick....really helpful in exams...stay blessed...from Pakistan

[@ghostfrom1950]

I love it when math tutorial videos say they're trying not to let the video go for too long. Meanwhile, that's what some of us want! That's the glory of KZbin, if someone is in a real hury, they can either speed up the video or scrub thru. The skip forward shortkey is "L", which is no problem at all. MAKE THEM LONG! As long as the video stays on topic, I want to learn damn it!!!

[@ricaulcastellon9615]

Crystal clear, very well explained. You are the best!

[@brehbrehgentil]

you are my hero, the index subtlety had bent my mind. thx u 4 unbending

[@CouldUseARide]

Got my final exam in 3 days. Thanks a lot!

[@patrickjmt]

+Nabil M good luck! Study hard!

[@derekfulginiti399]

love the conglomerate icon!

[@Vampirekat123]

How would the expression change if the function is f(x) = (6-x)^-4. or any other power that is lower than -3?

[@cediemacalisang7713]

You explain very clearly.

[@cakkuncaktinmilo4032]

u just save my day patrick..thank you very much

[@s.alizapiotrowski1474]

Thank you so much, Patrick! I am studying Complex Analysis and reviewing Series. This is very helpful!

[@lexengland6443]

Thank you so much! This explanation was super clear I’ve been having a really hard time with this topic and now I understand.

[@reaniegane]

When you apologized for the length of your video, I was just hoping that your video would go on because it is so good.

[@idbaronco4194]

Me has salvado amigo! muy buen vídeo, aunque no sepa hablar ingles te entendí perfectamente gracias a tu paso a paso bien explicito

[@MrHelpingHand]

Great video man! Thanks for all of the help!

[@rohith5062]

2:25 why cant i just divide by (1+x)^2 to get series sum for 1/(1+x)^3

[@nmpopa]

Is it necessary to change the index from the second series in order to compute the third one?

[@hengstar]

Very nice, man. Thanks for saving me from struggling

[@MrMultiMacedo]

you saved my life thank you so much

[@mistacoward7761]

That video was outstanding.

[@Rxpeme123]

I was wondering if you could help answer a question that I'm having a really hard time with. It asks to find the derivative of the summation from n=0 to infinity of (-1)^nx^(2n+1) / 3^(2n)(n!)^2. I have no idea how to solve this, your help would be greatly appreciated :)

[@miguelmanturano9108]

Thank you for taking your time to make this video.(:) )

[@jdilley00]

Patrick. Do you cull alot of your examples from the textbook "Single Variable Calculus: Early Transcedentals"? Alot of your examples match up =)

[@xlGotStridelx]

This is a great video, now if only you could use functions that didn't have a (1+x) in the denominator and instead had something like (10+x), that would be very helpful!

[@1hit2hitown]

+Martin Velarde all you have to do is factor out a 10 then you would be left with 10( 1+x/10) and continue as in this video.

[@cardinaltutor5711]

Thank you. This video helps me a lot.

[@sapphire9724]

BLESS YOU PATRICK

[@Daiz7788]

Do you have to change the n from n=0 to n=2 or can you leave it as n=0?

[@zo5796]

Thanks so much, definitely subscribing!

[@FlashFire40]

Hey, this almost exactly matches the book problem I just did. The only difference is that in my problem, a) was 1/(1+x)^2. Otherwise, exactly the same. So this is perfect. And yes, I also have the book Single Variable Calculus: Early Transcedentals.

[@reubenwilliammpembe667]

You are the best!!! Thank you so much

[@WifeSoup2]

Literally amazing.

[@katherineweinzierl586]

I'm confused as to how you got the part after the sigma. I'm trying to follow this and solve a different equation with the steps you use but I can't seem to figure out how to get the (-1)^n(n)(n-1)x^(n-2) or (-1)^n(n)x^(n-1) parts???

[@toddj.2]

Patrick, as a convention, can't we just increase a (the lower bound) by 1 every time we differentiate? That may be a more efficient approach, no?

[@Kitkat915e]

Just a question: how would you use these derivative versions to find the radius of convergence? Or would the radius be unchanged?

[@bryancabrera2702]

Kitkat915e I may be a little late, but the radius of convergence would in fact remain unchanged. However, the interval of convergence could change.

[@Kitkat915e]

Oh, thank you :)

[@6norcal9]

Patrick the book gives a solution to 1/(1+x)^2 to be the series from n=0 to infinity of (-1)^n*(n+1)*x^n, this differs from what you have, if you could please explain the difference it would be of great help. Thanks!

[@Bobboboll97]

Thank you, this helped me a lot!

[@TheBikhinkl]

I hope I will have a Calc teacher as good as you in college this fall. otherwise, my calc future will be bleak as in HS...

[@adammann6582]

a perfect math video 🙌 .than you Patrick

[@bayanashoori]

*You bring nothing but honour to your family*

[@yasothar4976]

If you dont change the index in part b (where it still remains from n=0 to infinity ) , would it affect your final answer ?

[@rachellee3050]

your handwriting is good

[@Ftom14cat]

hey patrick, this video is not included in your calc 2 playlist and it seems like it should be

[@coryfreestyle]

Thanks, you are the best!

[@berfin2523]

for b, if you initialize it from 0 then it will be same with c?

[@Sdollas]

WHY WASNT N=1 N=1 WHEN YOU DID AN EXAMPLE IN THE PAST, WHICH IS AFTER YOU TAKE THE DERIVATIVE OF THE SERIES

[@qasimaami9581]

o

[@mollyc2575]

Question. Would it be alright if I careless about the change of n=0 to n=2, and then comd back to n=0 ?

[@GodOfJazzDylan]

That's great, but how do you do it when it isn't (x+1) What you have shown is easy, but I have no idea to do it with, say, 1/(1+5x)^2 or x^2/(7+x)^3

[@perryleigh9028]

How did you get the sum from n=1 to infinity of ((-1)^n)(n)(x^(n-1) my textbook got (-1)^n(n+1)x^n

[@guiguspi]

Thx for the content.

[@williama.3193]

8:13 is there an add on? lol

[@loatilelebala6749]

THE GOATTTTT

[@rylanchinnock4871]

This is great!

[@xen05z]

3:40 no you can't leave it 0 because the stupid WebAssign homework grader will keep saying you're wrong. So you have to make n = 1, once you get you sum formula, change n to 0 and add 1 to all n's in your formula. I don't know, but that;s what WebAssign wants...

[@xen05z]

WebAssign and MasteringPhysics.

[@moozchi3]

hi patricjmt! can you please do 3 more examples for power series representation using differentiation and integration? THANK-yOU!!!!

[@that1guywhoknows]

If my calc teacher didn't point you out, I'd be failing

[@Misstewee]

Thank you thank you thank you!!!!

[@felixsamuel9714]

legend

[@lilliflower743]

Thank you!

[@byJayzik]

Radius of convergence?

[@AteenJoy13]

My calc teacher sucks, thanks patrick

[@that1guywhoknows]

I believe you try to get it into the form 1/(1-x)

[@anoniem012]

Thank you !

[@DonPasquale_]

I know this video is super old but does anyone know what to do if you have 1/(1+x^4)^(3/2)?

[@kylemorris371]

isn't that the taylor series? the taylor series is only for a_n(x-c)^n

[@Jayson8888]

shoutout pat

[@skategenie]

I can smell his sharpie from here!

[@brendanbramman]

Why do you keep changing how you write your twos!! It bothers me so! Great video by the way, thanks.

[@SlowKlone]

probably the hardest thing in calc 2 is this, im completely lost

[@KMBillah]

Why the calculus teachers don't watch these videos ? i mean they can learn the teaching !

[@leohe2690]

Really should have watched your videos earlier.. Now it is only little time before my exam...

[@cheeseisamarsh]

2 days until mine tragic

[@brucelee7150]

idk why but i keep losing him in this video

[@mehmetkurucu18]

2018?

[@johnperez3]

you forgot to derive.....

[@peeweewoen]

then u haf to differentiate or integrate it...look at his other video

[@poifquackula6665]

OMFFFGGGG so annoying! Please normalize the audio of your video before uploading so I don't have to turn the volume of my computer all the way up in order to hear you

[@patrickjmt]

no

[@Technolgy2]

:O

[@logoscafe]

[@fernandoalejo]

I hate power series

[@joeldevries2981]

Thank you!

[@AstreaChanellMen]