❖ Finding a Derivative Using the Definition of a Derivative ❖

[@BigTeix]

This guy is a better teacher than my actual calc teacher

[@emogirl1234567898765]

Agreed I finally understand

[@Gursewaksinghsandhu]

Kevin Layer Right bro

[@holdenvf]

Honestly

[@poop8867]

King Veli I guarantee that isn’t true. You’re probably just more comfortable learning on KZbin because you don’t feel trapped.

[@kaiynatjohn4147]

Same here 😄

[@LaraMcGill01]

Since (as I'm only a math lab instructor) I'm not allowed to give students my information to help them outside of class, I always point them in your direction. You're the best I've found out there. Keep up the good work, Patrick! You're more appreciated than you know.

[@TonyTorzido]

In seven minutes I learned what I couldn't in a week. Thank you.

[@m19petersen]

How many of you (like me) have a test tomorrow and are just now realizing you dont know wtf your doing :)

[@Dean444ful]

Hooray for the Procrastination Patrol! Join us today... Or tomorrow it doesn't really matter.

[@derekleighton7273]

Due tomorrow? Do tomorrow

[@malik789]

😂

[@tyesngates5607]

My final is in three hours :(

[@macarnott]

Hope you passed!

[@colinmchaney1142]

you arent kidding man I dont even listen in class anymore. I just go home and type in PatrickJmt

[@minibepbop5340]

9 years later I’m in highschool and do the same. How’s life bro?

[@Truck--kun]

why do i have to pay thousands in tuition when i can learn from better quality people online for free...

[@harshjha9795]

Haha I love watching these videos and then showing up to class looking like a damn wizard

[@nerseshamboyan8621]

you are so helpful. Im telling everyone in my class about you

[@patrickjmt]

that would be much appreciated!

[@Scorxcho]

That marker has such a satisfying noise to it.

[@MuffinMannTV]

you are the reason im passing all my math classes since 10th grade

[@asbestoscartoons8639]

swag

[@Kooks33]

Oh my goodness thank YOU very very very much PatrickJMT!!! You have no idea how much this helped me with homework!!! Please keep making more math videos, these are really lifesavers!!! Awesome job too by the way!

[@Orchiidify]

Your usernaaaame!!!!

[@kenkune55]

After being out of math for a year or so after high school, you've been a life saver as I'm starting off calculus this year!

[@maggiegrove5370]

You are the best! Helped me pass my pre-calculus class in high school and now my calculus class in college! THANKS!

[@skatexius]

Not only are you great at explaining but your voice also calms me down and somehow it gets me into "lets do math" mode. So, even if i do already know how to solve such problems, I just cant help myself but to watch at least one of your vids or art least have it as "background music" while solving :)

[@patrickjmt]

@FoolishTheMortal well, it is not the same cause this has a limit. : ) but part of the reason you see the difference quotient in algebra is because the person who writes the book knows it is important in calculus. the difference quotient helps us to approximate the slope of the tangent line by finding the slope of a secant line; we then take the limit of these slopes to get the slope of the tangent!

[@sagacity1281]

reviewing for AP Calc final tomorrow. I have watched a ton of your videos over the past too years and you really are an amazing teacher. Thanks for all you do!

[@shawndegroot761]

thanks so much Patrick! I made the stupid decision of taking calculus by correspondance and for the first 4 months I wasn't getting anywhere at all and was planning on dropping the course, and then I found your videos and finished the course in 2 months! You saved me $700!

[@musicjunkie225]

I'm usually decent at math but not when the instructor just throws material at you and expects you to learn it.You pick up where his teaching skills leave off and I can't explain my appreciation!

[@caswilso]

Seriously, patrickjmt, have I ever told you how much I love your videos? So. Stinkin'. Helpful.

[@Ambrynxx]

I really need to thank you. I have been watching your videos all year, and I just got 98% on my derivatives exams, all because of your videos!! You are such a good teacher, I couldn't of done it without your help. Thank you for doing this!!

[@antoinepelletier1182]

wow! this is magic! Within 7 minutes, I understood something my teacher didn't get me to understand in 2 classes! Thank you! this is a great video!

[@christiananton6655]

I've been watching and learning from your videos since 7th grade of pre-algebra. Now I'm in 11th grade taking AP Calc, and your videos never fail to teach me how to do my homework. Thank you for all you've done for me over the years!!

[@patrickjmt]

my pleasure! :)

[@koi2548]

years later and this guy still explains it better than my calc professor

[@bigchocholate03]

Dude.. I had medical problems this semester and missed almost half of my Calculus lectures. Just by watching youtube videos, many of which were yours, I learned all of the material I had missed. I ended up getting a B in the course. I owe you one.Thanks for the free help!!

[@noelcramiro]

perfect! I had this lesson 29 years ago..it's all coming back to my brain now..thanks

[@BoOkWoRmPJOiLuvLL]

I spent like 2 hours doing my calc hw, and asked other classmates and was still unsure of how they got the answer, but after watching only two of your videos, I know how to do all of the hw THANK YOU SO MUCH, YOU ARE AMAZING.

[@0kay651]

Bro, you're the GOAT of Calculus teaching

[@ccg1994]

I got my first A on a math test because of you. Thank you so much for all of your help! :)

[@dung-aocatherinep.6817]

Thank you for this video, this has been uploaded 12 years ago but it became a big help for me in this online class

[@AldosWorldTV]

at 0.31 woulda been helpful to quickly explain what the 2nd equation is for :)

[@amaniflood4726]

i think it is for the same thing. either equation will give you the same answer.

[@gappity]

you're famous now

[@lockedgamer8582]

yoooo bro you were doin this 6 years ago thats crazzy

[@morganlazar33]

I know that this a simple and silly thing to ask but can you quickly explain how to multiple out (x+h)^3? My Pre-Calc teacher taught us a simple way to do it last year but I can't remember now and it takes so much time on a test to do it out the long way! Thanks, you rock!

[@bwaa_bwaa]

Stumped by my professor and 4 tutors... I learned it from you in like 5mins!! 🙏

[@KidNamedLindseyy]

this makes me happy because i couldn't find a good video that showed how to deal complex fractions

[@ashleighkate94]

I love you! I couldn't figure out how to get rid of the h (my lecturer is ridiculously unhelpful) and this explained it so clearly and enabled me to finish my assignment! Thankyou :)

[@lexus14blacklist]

Big relief. Somehow I got hung up on this in class

[@ohhgeeme]

I learn more from your 7-12 min videos than i do in my two hour calculus class. thanks.

[@insanekrnboy]

wow i have a derivative test tomorrow and your videos just rock!

[@BreakneckWalrus]

I don't understand how anyone can dislike your videos! Through one watch of your video I understood the principles behind volumes of revolution, and my class is still just on definite integrals (which, by the way, I also used your videos for. Brilliant!). I'd always been fuzzy on the limit definition of a derivative (mainly because I transferred into Calc AB after my class had finished limits!), so I've been using your videos to catch up. Keep it up! :D

[@biancagarza3739]

YOU. ARE. AMAZING. Thank you so much! You have no idea how much this helped. My previous professors didn't think it was important for me to know anything about derivatives and you just helped me out so much on this Calculus homework. Definitely coming to see more videos from you any other time I have trouble. Again, THANK YOU SO MUCH!!

[@JimmyStartinStrength]

i didn't take calculus in high school but I am required to take this calculus course in university for my program and you're really helping me out alot, THANKS! :)

[@BaCkWeRdZ]

Thanks a LOT... I get like 90% of the way with a problem and your videos help get me over that hump... I am truly grateful

[@cd6581]

Does anyone know how he got (t + 1)^2 in the denominator at 6:30. I'm not sure where that came from considering he had (t+h+1)(t+1) in the denominator previously.

[@cd6581]

did he just forget to cancel h out from the denominator when he canceled h from the numerator in the previous sequence? Having to cancel like terms in both the num/denom of the function by h 6:05

[@kristen4677]

Colton Davie he substituted in 0, anything plus zero is just itself

[@anthonyjh02]

When he plugs in Lim ( t + h + 1 ) ( t + 1 ) h->0 The h is replaced with zero, making it Lim h->0 ( t + 0 + 1 ) ( t + 1 ) In other words it becomes Lim h->0 ( t + 1 ) ( t + 1 ) That’s just the denominator

[@Ephesuz]

you just saved my life! Exam in 5 days and I really needed this!

[@tobychow4761]

thanks man! Cramming for an exam thats in two hours, your vids are a ton of help

[@patrickjmt]

@skatexius always happy to help out someone that likes the stranglers (good for you!)

[@yasminmaefernandez8533]

exams today and I'm looking help for derivatives and I stumbled on your channel, you really literally helped me! thank you!!

[@Jishory]

Once again I couldn't understand until I watched one of your videos. Thank you so much. You're the man!

[@eckoecko95]

Thanks for the help man, your videos are actually well done. You have no idea how helpful this was.

[@jome1996]

This is very well done glad you made it

[@shvideo1]

Great educational video. I am polishing up my math many years after college, and I find your videos excellent. I am developing a love and fascination for math. Thank you.

[@Corrup7edChaos]

I learn math so much more from you than any other math teacher. thanks :)

[@joslinnick]

I can now see why those who struggle with algebra struggle with Calculus.

[@patrickjmt]

ya, i will try to do a video this weekend!

[@xLithePanther]

Thank you. You're seriously a life saver. Become a math teacher! So many are just so shitty at it.

[@pyromaniac946]

you just saved my grade :) i think i have the worst precalc teacher on the face of the planet, you just explaned to me in 7 minutes what hes been trying to teach for 2 weeks

[@patrickjmt]

@SirNewtonLeibniz change in x / change in y. you do not treat variables like constants, except when taking derivatives. you are finding the rate of change on a 3d surface, parallel to the xz plane or the yz plane, in which case either y or x are fixed.

[@patrickjmt]

@anikazangel1 no, i think this is the only one i use

[@Lexyvil]

I don't get the part at 1:09. You substitute the "f" by 12+7? What about the (x) that comes right after the "f" of the second term in the numerator? Why does it go inside the brackets?

[@Mrpostalguyperson]

dude this helped so much, I'm glad u explain things so well, like you understand there may be basic steps we don't remember but regardless thank you so much man

[@abhisingh2065]

bob hendryson 6

[@1904home]

very cool. been out of school for 10 yrs now and i'm going back to school for a BS in Math and so i am just studying up online before I get into my Calc for the first time in a long time. Is it just me or has the internet just exploded with knowledge in helping folks learn topics like derivatives and limits? I mean, it is absolutely crazy. I can get online and learn from a dozen teachers the same topic. Back in the day, it was just you and your teacher and if he/she wasn't any good, oh well!

[@holdenvf]

Tell me why I come home everyday and search up the topic we learned in class and don’t understand it until I watch the video

[@kururumega]

I love it when the stuff I learned at the start of A-level gets explained in a more technical and clever way

[@amethyst6386]

thank you so much for this video, I watched so so so many videos on this (even on my native language) and none of them explained it as clearly as you did. Thank you so much for doing this for all of us

[@compendiumcharlie]

Oh my gosh! I needed this on a test and I had no idea what it even meant! thanks this video has been really helpful!

[@mattew8978]

Patrick you are so much better than those videos which show only the half way of their calculation and steps. Then ask us to buy for the remaining 1.

[@rosiecouture1]

Thank you so much for your videos...I have my biggest/most important maths exam of the year coming up in a few weeks and your videos are really helping me consolidate and revise everything :)

[@PNKEEE07]

you did way better at explaining this than my teacher. and i'm in business calculus in college!!

[@guardianxavi]

Thank you so much, I wasn't doing good until I follow your videos.. Thank you so much ! !!

[@stevenjonas1]

This video helped me 2 years in a row lol thank you my dude

[@patrickjmt]

@Corrup7edChaos u r very welcome!

[@StupidSpoge]

Thanks! I have my final tomorrow... These types of problems have been bonus questions on every quiz and test, and I never bothered to learn them... haha They're easier than I thought! I owe you one.

[@aienafatima1700]

Mans explained the concept better in the first 2 mins than my tutor did in 30 mins.

[@muscularclassrepresentativ5663]

Patrick my man, coming in clutch the night before the ab calc midterm for all the stuff I forgot

[@user-sp9ue1ws7c]

Tom Danner I'm doing the same thing right now

[@fuckaudolphin2591]

patrickJMT solving problems in sharpie since mid2000's

[@kickit246]

I can't believe you posted this video back in 2008 and your still active on it! Its almost been 4 years... I'm glad though :) PS - Calc final in 2 days, 26 minutes :(

[@nutacorn]

This was actually an exact problem in my homework. Thank you so much for helping me understand!

[@tariroalfa]

you literally just saved my maths grade:)

[@henum007]

Sir I am learning so much from your videos. Thanks for the efforts

[@SKDNHEL]

Thank you sir! i've done my homework because of this video.. GOD BLESS YOU!

[@hio777]

Thank you, your examples are awesome. This one of the best way students can learn: threw many simple examples. We must build the foundation before we could add to it.

[@power-max]

The other day I was goofing with my graphing calc, and since it was a phone app and had no derivative function on it, I decided to invent it! What I did was I took a simple parabolic function, and everywhere there was an *X*, I made it an *(X+1)*, and graphed the 2 functions *(x+1)^2+3* & *x^2+3* Then I subtracted the 2 functions into each other to so it graphs the difference between *X* and *(X+1)*, and this was what I called a 'poor-mans' derivative. The problem was that there was significant error in the output of this, so I attempted to fix that by making this *1* term super small (like *0.00001*) so it I can 'hone in' on a very small portion of the slope of the parabola) but then the output was very flat, not as pronounced as it was supposed to be. I had to figure out a way to amplify it by that *0.0001*. I did this by multiplying the entire thing by the reciprocal of *0.0001*, or *1/0.0001*. So the only difference between what I figured out and that you show here I have never learned limits, and so my process was a bit more convoluted, as I just used the smallest number my calculator will allow. I can't believe that I pretty much figured out how to do derivatives all by myself, who has not even finished precalc! Although I still don't get integrals, they still scare me lol!

[@cartersuppes9434]

Thank you sir. Much better explanation than my calc professor

[@miltonlaxer]

So if h isn't being multiplied by anything you can just set it to 0 cause it approaches 0? Is that because the entire point of what we were doing is to get the denominator to not = 0?

[@copycat487465]

yes

[@QuetzalUlisesOrion]

thank you from Mexico dude, first time I see the explanation of this.

[@Mungkar11]

I thought I'm gonna lost my mind thinking about derivatives because you know my instructor is kinda rapper when it comes for teaching us. Thank you by the way...

[@BitterSweetBleu]

You really should be honored by youtube in some way for helping all of us out, thanks Patrick :)

[@AlexBeEditing]

I keep falling asleep in class and missing the important steps... thank black jesus for your tutorials!

[@adityamukherjee9462]

thank you, i had kinda forgot how to do this... but you revived my memory

[@mcdonough87]

I like how you put the dots for your i's over your m's

[@patrickjmt]

not sure what the 4 step process is

[@tylersargent3307]

thank you so much! I'm struggling so much on this subject in calc and you basically answered all my questions!

[@LanimeFan]

Thank you so much for the videos! Math is not my favorite subject but your explanations are making it easy to understand. I really appreciate it :)

[@keeler1160]

The only thing I do not understand on the numerator how he got H for (t+h+1).

[@lusinzotepa7620]

keeler1160 I can help if you explain your question better

[@Perish1]

I think he might be out of school by now

[@megaabomin8r507]

might've failed maths due to first principle struggles...

[@patrickjmt]

@mypinkdollprincess happy new year to you too! things are so far, so good! i hope the world is also treating you well.

[@xdontfadeawayx]

Can someone help? I'm still confused as to how this applies to other ways of taking a derivative like the power rule, product rule, chain, etc... for ex., why does y'=nx^n-1 when y=x^n? Why do those rules work?

[@daisdais508]

You made me love math again! thank you! College was making me hate it and I have always enjoyed it, the way my professor explains things is so complicated :/

[@ericolvera496]

You're a life-saver man, thanks.

[@ThePonandzigirl]

Thank you so much! I blanked out on this and seeing your video everything made sense again!

[@Kswish91]

this was killing me in my class. thank you so much.

[@Anonymous2094]

Thanks a lot Mr. Patrick for your useful vids. :) Very Helpful.