Derivatives - Product + Chain Rule + Factoring

[argon101v]

thx a lot dude, realy helpful!! saved me in edexcel exams

[megacoolkid94]

studying for my calc exam next week! My teacher is terrible so this helps a ton!

[stinggrand]

Tnx pat ol I need is how it be factored.

[missRilush]

Please let me marry your brain :P

btw Perfect tutorial....

[eelwell41]

patrickJMT needs to be a Professor i have learned more in his videos than the whole semester in a lecture. Absolutely amazing, my teacher needs to see this before your videos make her obsolete

[tiggerie345]

This is exactly what I needed! I'm still groggy on derivatives and my AP Calc AB class is on derivative tests. I'm trying to not fall behind and you have helped so much. :) Thanks.

[bbygirllyssa]

thank you soooooooo much :') this is really helpful!

[patrickJMT]

@bbygirllyssa no problem!

[vikalpofficial]

to the 7 dislike and rest, ask if u have a query like others and don't dislike the effort of someone which is an absolute blessed work.

patrickJMT thanku very much.

[patrickJMT]

@vikalpofficial you are very welcome : )

[ronsiew]

I'm doing the iGCSE Further Pure Maths course, this helped me so much!

[PIMPMASTATREX]

The best thing about your videos is that they are ALWAYS here. I have a second midterm tomorrow and this is just the refreshing I needed. Last time I used your videos to Do one last study session I got an 80 out of 100 (messed up on the small things, small errors, not the concepts :]) hopefully this time it goes just as well. Word problems have me worried though, I can't find any of your videos that use continuity as in growth or decay etc but I have my notes for that. THANK YOU!!

[1395mattmatt]

Thank you so much :D had a mental blank during study o_o

[Canute87]

God Bless Youtube

[patrickJMT]

@Canute87 and patrickjmt

[BoomitsStacie]

What if that x^4 at the beginning were a cos^4? Do you have a video like that?

[jkStephanielolz]

i wish u were my ap calc teacher! this helped so much! my teacher likes to skip steps which confuses the heck out of me.

[patrickJMT]

@jkStephanielolz come back and watch any time : )

[jkStephanielolz]

@patrickJMT i definitely will :) thx

[boomboxxking]

seriously... you just saved my life. Thank you so much. You don't know how much you just helped me. I thank the Lord for you :)

[Drakononous97]

Where does the initial 5 come from when you are doing the product rule?

[flingnfly]

@Drakononous97 the five is the derivative of the base you apply the chain rule to

[Prof16440]

why do we need to use both chain rule and product rule?

[patrickJMT]

@Prof16440 cause there is a product and a composition of functions (the stuff being raised to the power)

[Yotuber006]

Thank you for uploading these videos. They're so helpful!

[patrickJMT]

@Yotuber006 my pleasure : )

[alf0004]

thanks! I feel ready for my exam because of you!

[SarahIsShameless]

a tutor at my college wasnt as good as you are! thank you so much!

[patrickJMT]

@SarahIsShameless well, i probably have a bit more experience than the tutor at your college : ) 

[ehgp99]

im trying to understand how you got a + for the second step

[AlexShelden]

@ehgp99 He used the product rule in conjunction with the chain rule.

[chentity]

thanks! :)

[twinturbosilvia]

wow my teacher took up the whole white board to explain something so easy which confused everyone! Great example here!

[nessquik95]

didnt want to follow ur tutorial just in case ur method was different to mine and made me more confused so just used ur question, completed it and checked it and it was correct :) thx

[AMGrevolution]

If I pass calculus, graduate, get a good job, and become rich. It will be all thanks to you

[vusiliyK]

THANK YOU SO MUCH you saved me from a lot of frustration. I kept wondering why i was not understanding the books answers...its because i was only trying to simplify, not factor.

[Joanaavila1]

Why do you multiply by 5 if you are already taking the derivative of [5x-1]^3??

[sweentnhot0104]

@Joanaavila1 (5x-1)^3 can be understood as 2 seperate entities, the outer one, which you conclude as u^3, and the inner one, which you set u= 5x-1. The product rule states that you must multiply both the outer, and inner dy/dx, so you must take the derivative of u^3, which in this case is 3(u)^2; plug in u=5x-1, and you'll get 3(5x-1)^2. Then, find the derivative of the u itself, which is 5 (remember u=5x-1). Multiply all of them and you're good to go!

[Dwnfll12]

thanks

[lloret009]

i love it, i can understand it now.. when my was teacher explaining this i cant seem to it together, i was like FML!.

[o0mohammed0o]

I have a midterm tmr :((((((

[keraito]

I watched some vids of you and they're really helpfull. I understand everything you explained :)

But I live in the Netherlands and we never used the [square brackets] yet so I wanted to ask what the difference is between (round) and [square] brackets?

[medkidrocker]

You are my savior...

I fell in love with you (dont care you're married) from the first time I saw your vids

You are awesome..

I wish you are here with me..

You are my king and my prince..

I love you, Patrick... xoxoxo

[mishyxoxo]

saved my life man

[chadhall83]

wow u showed me something my teacher is hiding from us! thanks!

[carlottafy]

AHH! you are saving my life right now. Thank youuu! :D :D

[dragonmaster84]

Where the hell have you been all my life?

[mickeyrockstar77]

Great video...



[banderso4571]

Dude! This is awesome! You should get paid for this! You should at least get paid enough to use whole sheets of paper. Whole sheets that don't look like you found them stuffed in the bus seats on your way home from school.

[patrickJMT]

@banderso4571 ha, yes - this was a very early video, made quickly for someone!

[toda9008]

when you did the chain rule for the second part i was with you until you multiplied by 5 my question is where does the 5 come from Imma take a wild guess and say from 5x but im not sure plz help my prof sucks ass we've been doing derivatives for past couple of weeks and he just mentioned chain rule 2day and was like i didnt go over this wit u Oh. And his explanation didnt make any sense. Please help me............................­...

[toda9008]

@toda9008 never mind i got it 5 comes from the derivative of 5x-1 :)

[Elquiesceace]

why do you mutliply by 5? where the hell does the 5 come from

[patrickJMT]

@Elquiesceace outer space

[lolkiwi]

@patrickJMT

Why didn't you answer his question? I was wondering the same thing...

[herolegend16]

@patrickJMT lmfao!!! ....XD

[toda9008]

@Elquiesceace 5 comes from the derivative of 5x-1. I think cuz the derivative of 1 is 0 and the derivative of x is 1 so 5 times 1 is 5

[Dirtbiker1537]

@Elquiesceace its the derivative of 5x-1

[ilave2ski]

@Elquiesceace the 5 is the derivative of the term inside the square brackets, [5x-1]

[redrum41987]

@Elquiesceace the 5 came from him taking the derivative of the base (5x-1).

[nessquik95]

@Elquiesceace its the derivative of (5x-1)

his way is a little confusing cause he does it in one hit i separate mine at first to get derivatives then i put into product rule

[jsm832141]

I LOVE YOU BRO.!!!!!!!!!!! My teacher sucks at teaching you just saved my life.

[LeafFan0016]

Thank you so much!

[Killuminatismd]

omg patrick...tommorows my test...and i was looking through feeling like i know everytthing...then remembered the teacher said that we have to do complex product rules! i was like omg...i started panicking. Then i remembered you, and came to this video with a big smile. Now im leaving with a bigger SMILE! THANKS PATRICK WE LOVE YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!­!!!!

[JmoulFrancis]

THANK YOU PATRICK!!!! The tricky part was a bit confusing to me, but you made it all simple and now I have more lines to work with!!!! you're a life saver!!!

[alicetex]

so, the video was cut short as it was getting interesting, is there a second part to this video? Thanks

[nickh186]

My teachers use an online book and homework setup and they must have been smoking angel dust when they wrote the book because it makes no sense at all. Thanks for the video, clarified everything.

[immigrantinc]

PatrickJMT! You are the Jesus of Maths! I was cracking my head over this and from you video I understood 2:53 minutes! You should win best math teacher of Earth award.

[shenakarl]

HEEEY, I LIKE IT WHEN YOU SAY THE WORD "ALONE"

BTW. THANKS. IT REALLY HELPED ME ALOT. TOMORROW WE'LL HAVE A RETAKE

BECAUSE ALL OF US IN THE CLASS FAILED IN THE EXAM :)))))

[changeisnowpeople]

i can teach better than you.... hahah... i hav a better and easier way....

actually derivatives is easy

[patrickJMT]

@changeisnowpeople that is wonderful then! i never said i was anything special that i recall. you can feel free to also make some videos and share your wonderful talents to the world. otherwise, you are just trollin' on the internets...

[Scatteril]

why we multiplied it by 5 ?

[yiyp]

do u get paid for this? cuz u deserve a good salary for this man better at teaching than any1 in my life

[china2207]

please please can u post really hard optimization problems? i would greatly appreciate that. my teeacher likes to make them really hard.

[evhsrvfe]

Thank you so much!!! That has to be the most concise explanation of these type of problems so far =]

[kaliwete19]

thank you! thank you! thank you! it helps me a lot!. and you make it easy! thanks

[yumyumsamvich]

You make it so simple and easy.

[lllUSlll]

you are my crush,

[goplaysoccer13]

You have saved tens of thousands of kids' calculus grades. THAT IS AWESOME! :D

[kiwida]

Thanks a millions i watched a lot of your videos, they help me a lot. Thanks man. Great work, hope you really become a professor and save tons of people from horrible monstrous mathematics professors!

[dipstick555]

you make reviewing easy *hugs*

[evilan9el]

I hope you get paid enough to do this, cuz: YOU ARE SAVING THE WORLD, ONE EQUATION AT A TIME.

Noh, really.....

[patrickJMT]

@evilan9el haha

[Slimnplatinum]

wow! I just went from being totally lost to actually knowing what to do! Great!

[0ecml0]

saved my life!

[LorencHoxha]

Great explanation! That's what I needed! Thanks!! :)

[karl16laker24]

You are an AMAZING person!!!!!

[sandra17143]

how do you solve

y=the square root of 4x+sec(1-tan(2x))

ive tried and tried and i get more and more confused!

[jensbuhler]

Really useful, now I don't have to copy my homework last minute :D

[dragonmasta91]

heya patrick brao, if you can, can you plez make more videos on factoring especially when during sketching a graph, because alot of ppl i know including me, has problems when you have to find the critical points after factoring

[omarhea1]

How do you solve this? I'm having trouble

4x^2(3x-2)^5

[mvenom101]

@omarhea1

Solve? or differentiate and solve?

[moonofsilver]

Dude! This is sooo helpful! I have summer homework for BC Calc, and I had a problem somewhat like this and the factoring out actually gave me the answer I needed! THANKSSSSSS. :D

[like9orphanz]

How did you ever get through college without being able to watch your own videos

[kma24kai]

I wanted to say thank you for clarifying things up with your quotient rule and product rule videos. I have my final tomorrow for pre-calculus and we rushed this part before classes were over. Thank you very much!!

[ShrimpRamen]

can you do one of where the exponent is a piece? I have a complicated one with E raised to the W^2 power that I cant figure out

[ShrimpRamen]

You know what I love about your videos? You get it. Math books, professors, study guides and even webpages will skip steps without explain them, and for instance factor without saying that is what they did. They expect you to just extract the steps like simplifying and factoring, which they leave out of the visual examples written on the board, textbook examples ect. They just through in a row of like three steps, and skip the fundamental algebra part. How does that help us? Thanks, youre great!

[Chewyrasp21]

thank you so much! your videos have been of great help, i get a clearer view :) hope there are more to come

[mypinkdollprincess]

Great Just great! thanks!!!!!

[xstncd]

My teacher is my head of maths but even she does not explain as easily and clearly as you ~ Thanks Man :D

[patrickJMT]

@xstncd glad u like my explanations!

[Randomjo]

A quick question, where did that extra 5 come from at the beginning?

(5x-1)^2(5)<this one when you just finished the product rule

[Chris5574]

@Randomjo if you're talking about his first line of work there, that extra five is the derivative of what is inside of the square brackets (namely 5x-1). That is using the chain rule. If you still don't understand look at a video that explains how to use just the chain rule.

[pr3tywoman09]

You are awesome!!!! I lean more here than in my class or with books or even with a tutor, I can replay, pause fast forward and its awesome! You explain soooooo well

Thank you for the videos!

[lerWHOOPWHOOP]

yay for left-handers!

[vitthal2001]

Wow you explain things so clearly, thank you :)!

[Koinodrama]

you just SAVED me, thank you soooooooooooo much. Keep up with the great job

[thewreckedup]

U ROCK MAN! :))

[pjsierra1]

Awesome video

[ChaseSceneMusic]

God. I love your videos so much. I paused this one and did the deriving in my head before restarting it just to see if i was doing the steps right. I was. Because of you. Haha.

[chocolatecookie77]

i luv you honey!

[amjPeace]

Whoops! Looks like I have to go back and review the chain rule.

Thank you very much, Patrick!

[karlkarlkarl1234]

You should tutor Alex Jones in mathematics :-)

[AwsomestKill]

alex jones needs a psychologist more than a math tutor

[heyyhowyadoin]

im gonna miss you when i go to college

[patrickJMT]

they do not have the internet there? : )

[malakov5]

ah, I see you just factored out an x^3 without distributing things confused me at first, but then again I also have no sound. Thanks for a job well done.

[IchigoBubbl3]

I LOVE YOU! That was so clear and concise and so NEAT! You're so awesome for doing this.

[MrAthos909]

Thank you so much, youre the best!

[222abboud]

y did u multiply the first step by 5 i dindt understand :S

[gamesbok]

5 is the derivitive of 5x-1

[starmate]

Dude I owe you for this... THANK YOU SO MUCH (Y) !! :D

[themonster36]

thx man

[rednebula317]

Thank you!!!!!!!!!!!!!!!!!!!!!!!!!!1

[zo0yoRk69]

great stuff. but one question. you take the derivative of the x^4, leave the inside alone, then multiplied by x^4 times the derivative of the inside then last multiply by the derivative by the inside (5). why dont you take the x^4(5x-1)^3 along with the 5 like in the previous steps?

[CanadianChamp01]

Thanks dude now I can go on easily with mathematics in college (CEGEP dans le fond)

[bridgetc744]

THANK YOU!!!! I finally understand my homework!!!

[jajaja295]

Just subscribed, you are like the light at the end of the tunnel

[Neelufaar]

very helpful! thank you for posting this video, i am unstuck from my calculus hw :)

[awells88]

Excellent! I was stuck on the process I was supposed to do first. :)

[vilyar122]

omg tyvm!!! i forgot how to factor with the product rule haha

[Kakashinoor]

Have I ever told you that I love you?

[patrickJMT]

i am not sure...

do you? : )

[RooneyRULZ12]

Ur videos rock, just suscribed bro

[ouzairhafeez]

nice......thanks a lot ...........

[slai89]

why does he multiply with 5 in the second row

[DeJayHank]

Because its the derivative of the inside of (5x-1)^3, since the chain rule requires you to do that aswell as the derivative of the outside.

(5x-1)^3 = 3(5x-1)^2 * 5

just like in the video.

if you still don't understand then i suggest visiting his website and checking out the videos about chain rule.

[Chiverra]

solve f(x)=x sqroot ( 8-x^2) please!!!! T.T

[ma3828]

are you actually teaching at university?

[saggigirl01]

what schooling level is this? please tell me it's not grade 12/senior.

god i dont think i can do this!

[Chafezi]

Not that hard, no worries.

[aranda89]

Wow! Detailed explanation and perfect writing. It's like learning my abc's! A+

[pearlsea]

Thanks for this video. In my calculus class I can do derivatives with no problems but cant factor so well.

They need to call it advanced factoring with calculus.

[patrickJMT]

algebra is what dominates most people in a calculus class...

[dorothydorothy111]

dude! you are the best video teacher on the entire web!

thanks 4 the help :-)

[patrickJMT]

happy to help my friend d - squared one one one

[Multiplelayers]

Did you forget to tack on the +15x at the very end?

[patrickJMT]

nope! i simplified inside the brackets to combine all the x's to get 35x

[GunnersOwnAll]

bro i am subscibing to your videos.. they are amazing

thanks

[6588245]

hey patrick, to get the 5 in the second part of the equation in the f'(x), u did the derivative of the inside which is (5x+1) to get it, rite???

[patrickJMT]

yep! thats right!

[Chris5574]

@6588245 that's right

[MundusLitterae]

You know, I think it's the factoring that confuses people. I was going over an example problem like with my friends and they were wondering how to simplify it. The answer was factor!

[patrickJMT]

yep! usually it is not calculus that gives calculus students trouble, it is algebra!

[lalsad]

you do not understand how long i have been sitting here looking at my notes and book trying to figure out how to simplify and factor a problem just like this. thanks you SO MUCH!

[patrickJMT]

no problem!

[Ixhatexthisxlife]

Amazing. Thanks for all the help... This video makes so much more sense! I couldn't find help with this from my teacher, book, notes, supplementary website... nothing.

~A.

[patrickJMT]

glad it helps! always nice to see things 'in action' vs. having to read it all and sort it out. i have over 200 vids on my website too!

[yoko180]

Patrick, I need to understand this particular function. More specifically how to factor out and simplify negative rational exponents. I need as much detail as possible. Do you think you can post a video working this equation out for me? I'm not just trying to get you to do my homework. I know I don't have to use the chain rule for this one. Here it is: f(x)= (2x+5)/square root of x

[patrickJMT]

i may be able to show u in a day or two... i have 13 hour day today and i get about 20 requests a day for this : ) maybe someone out there can help?!?!

[adeyinkaodunfa]

respec all the way from jamaica seen, buyakah

[patrickJMT]

nice! jamaica! when i come visit jamaica, we go out and paint the town 'green'! : )

[meatyfishman]

thk u sooo much, amazin

[orion5893]

I've been looking all over the internet for an example like this one. Post more complicated examples like this one. Thanks for the help, your awesome!!