❖ Sketching the Derivative of a Function ❖

[@patrickjmt]

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[@henryle4407]

The moment when you realize that learning on youtube is more effective than learning from your actual teacher at school Thank you for saving my life!

[@mikegarcia2279]

Agreed. Bless this video

[@APSEAPSE]

So true

[@brymetheous2387]

Yeah agreed, it's like my math professor just teaches me what to look up

[@CollaborationSTL]

10 years later this man still saving us

[@gautamdatta8194]

11 years now :D

[@bobjoe164]

like for real man God bless

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FOR REAL

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Fax

[@kendyllb7400]

make it twelve

[@ST5S5]

You taught this to me in 15 minutes better than my math teacher could in an hour. Thank you!

[@sebon11]

Same here

[@vpkasar7858]

yall are old

[@StephenRayner]

At around 5:38 I got slightly confused for a few seconds. To me you had your pen pointing down (i.e. negative) but you was saying it was getting more posative. But then I remembered we consider the direction from -x to x. so if the line is going from y = -5 to y = 5 from left ro right it is increasing and so is posative. If you consider the other way then you have negative but we consider from left to right. Hope this helps others who may have been slightly confused for a second.

[@LiOnHeLl-kc8vy]

yea i was so confused. Thanks for the heads up.

[@alexmorgan4220]

Thanks >3

[@gabrielamendoza4489]

😁

[@РомаШило-ь7й]

I want to point out in the first example, the graph is a cubic function. We can arbitrarily say x^3. Using some basic calculus rules, we can say the derivative of x^3 is 3x^2. 3x^2 is a parabola. That can help you identify which graph is the derivative. =)

[@trixiefortich3142]

"sorry for my bad graph" wait till you see my graphs....

[@fyzy123]

You are so much more helpful than my own professor. Can I pay you instead of her like seriously the class I'm taking is bullshit

[@patrickjmt]

Works for me! Seriously though, sorry your class sucks!

[@caseysheehan3182]

+patrickJMT But seriously you just helped my roommate and I with a quiz, TAKE MY MONEY

[@dannyzuko1850]

This probably won't mean a lot with the countless 'thank you's you receive everyday, but I seriously want to thank you. This is EXTREMELY helpful. Bless YOU!

[@whywasiborn851]

Your vid popped up on KZbin for the first time in a few yrs and I just wanted to let you know you pulled me through HS and College.

[@ilikedetectives]

Thank you so much!!! My teacher skipped in class this part and now I'm having trouble with doing the hw. You just saved my life!!!!

[@SuperKilltacular1]

pretty sad when your instructor sucks at teaching and you have to come here just to learn how to graph a derivative...

[@1MrShiny]

you taught me in 10 minutes, what my textbook couldn't teach me in 2 weeks. You are a miracle, i suddenly feel more confident about my upcoming test. Thanks!

[@Countrycon]

You are hands down better than any math teacher I've ever had.

[@patrickjmt]

that is a nice turn-around grade-wise : ) glad the vids helped

[@Marina-zn8ip]

This was so helpful!! Have a calculus exam next hour and this video has been way more productive than anything my teacher ever said.

[@rotate58]

I can't thank you enough, your fantastic explanation and teaching method helped me to understand what close to three hours of confusing instruction with my own teacher could not. Thank you!

[@SammyWinFL]

@patrickJMT A great teacher like yourself will surely be repaid for their good deeds as a person in one way or another! I'm studying for the PCAT exam and this helped so much. Thank you Patrick

[@devanmauch7843]

wow you really cleared this up for me, thanks! I'd been struggling for so long trying to understand what the point of this was, and now i finally get the y values literally represent the slope value of f(x).

[@patrickjmt]

yep, that is all it is!

[@uriellopez6529]

It's been years since I've been in school and I'm returning in a couple of weeks and your videos have made me confident in my math skills once more!!! Thank you so much!!!

[@xxpunkxxgirl]

Awesome!! We're doing this in calc now, and you taught me better in 15 mins than my teacher did in a whole week.

[@elyazzoo]

hey i really appreciate this my teacher doesn't really fit my learning style at all so you are literally getting me through calculus

[@puckSHOCK]

I started Calculus a month ago, in that time, I think I've watched a majority of your calculus videos. Thank you for saving me :)

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calc final in 2 hours! this is a great review

[@fe.rya.lazeem]

so how was the final lol

[@randomstuff940]

@@fe.rya.lazeem LMFAO

[@mirandashirley4697]

Thank you so much! My teacher flies through our calc lessons so this helps TONS. I really appreciate it.

[@DeJayHank]

failed my first exam. 2 months later i had another chance. used your tutorials for 2 days and got top grade. thanks alot mate =)

[@PRDZ110]

15 years later and ur still the goat man !

[@macallancruff2828]

I have a crazy math teacher who looked at me like I was crazy when I asked her what the heck she was doing. Thank you so much for clarifying! Keep being awesome!

[@mf7114]

Thank you so much! I am in calc my freshman year of college and even though I go into office hours and such, I had NO idea what was going on. Thanks for explaining it in plain english and not some fancy math lingo :). You're awesome!

[@patrickjmt]

ya! that is probably possible! i will try to make one later today if i remember and dont get lazy! (gonna be a beautiful day today... dont wanna be inside making math videos!!) : )

[@TheWarfare07]

this is great. i learned so much more in 15 mins than being in class for 2 damn hours. thanks

[@lizzyjane1361]

THANK YOU! 6 days before my mocks and I was freaking out about this. You're my hero :)

[@hartake6667]

Boss! With just the first 5 minutes I've been able to make deductions to answer 5 questions on the assignment correctly.

[@EmilyDeibert]

You probably just saved my life for my calc test tomorrow! Keep up the good work!

[@Boombocks_Studio]

Over 11 years since you uploaded this video, but thank you for it. My professor is FUCKING DOGSHIT and not teaching us, instead relying on the eText and short "lecture" videos from the code for our required materials. It's pathetic but I'm learning more from your content than anything in this $200 book code material.

[@joshuahurtado882]

dude, well done. I finally understand this concept, my instructor tweakinggggggg.

[@Dean444ful]

Can you be my calculus teacher?

[@xueyiwang9738]

mitch-bittens 😂

[@mangalamokashi9908]

mitch-bittens he already is😁

[@rinarox912]

i just realized you're left handed!!!same here! you're good at not smudging over what you write!!! I always end up smudging whatever I write on the board because my hand just goes over it haha and thank you for the video! it's very helpful

[@OverlyCuriousEngineer]

You sir, are the best tutuor to ever step on the face of the earth. Hats off!

[@memirandawong]

Well, you have rendered my calculus book astonishingly useless with your videos! That's okay. The only thing I still need it for is the assigned HW problems!

[@madelyndriver1213]

Thanks for the lesson. I got a high fever the second week of classes and am trying to teach myself Calc before classes start again on Tuesday. This helped a bunch!

[@Beauty_by_Summer]

omg sir u dont know how much youve helped me! im a senior in high school and im taking AP calc, the teacher never explains stuff! but u made it much more clear. thank u!

[@kingsley182]

Desperate attempts have led me to the internet. I found your video. THANK GOD. I AM GOING TO ACE THIS DERIVATIVE GRAPH IN MY MATHEMATICS EXAMINATION TOMORROW. THANK YOU.

[@patrickjmt]

@rosepetals1002 u r very welcome

[@sakaklovas]

Um... you just taught me in 15 minutes what I was struggling to learn for days...thank you.

[@CL-lr9wh]

I spent three semester on calculus and didn't know how to sketch this. And you helped me just in a few minutes. Thanks!!!

[@mattreese]

I've watched many of your videos, they are a huge help. Thanks for breaking it down into lemans terms for me.

[@0bsessionist]

You're better than my calculus professor! Thank you so much!! You're saving my grade!

[@scribbledheartz]

This made a hug impact on my graphing ability. In my calc book there's questions but no explanation on how to go about graphing derivatives of a function. So thank you!! :)

[@patrickjmt]

@Xx0Mystic0xX i will also post it as a video response in the comment section

[@valkyrie034]

Thanks for the help, keep the videos rolling. First semester Calculus, and was having trouble with graphing them- couldn't wrap my brain around it, but I've got it now!

[@patrickjmt]

@PSliveNlove happy to help!

[@lizbizwiz1238]

Dude, I have a Derivative test tomorrow and you are a lifesaver!

[@PossumPog64]

2023 and this man is still saving the lives of all STEM majors

[@keithbt430888]

this makes graphing derivatives seem too easy, i hope the school you teach at really appreciates you. :)

[@juliankashama1279]

Hey Patrick! Thank you for helping me with my engineering degree. I feel like I know You! We spent long math nights together. 🤣🤣Graduated last year. Just want to saying thank you. You have a God given gift! You helped me out big time!! Thank you. Writing from Botswana! Much love!

[@patrickjmt]

Happy to help!

[@helioselenus]

Awesome. Maybe the title should be "Finding the derivative of a function graphically." It took me awhile to find the right video. Thanks.

[@patrickjmt]

@MrAznSoldier thanks for taking time to watch my videos : )

[@vishalmishra9214]

after 15 years still you are best in this domain.🤗

[@MrCaRTom]

i have a math test today in a few hours, been watching your videos for the stuff i had trouble with and since i went over them so much, that's the stuff i feel better about :) i hope i do good on the test..

[@LilbabyonYT]

I hope you aced that test. How’s life?

[@shahadmerani3116]

the graph I’ve been struggling with for 3 days..u basically saved my life lol 💀

[@TheTastyAsian]

Omg you're such an amazing teacher!!! I've had at least 5 different ppl try to teach me and I still didn't get it--but YOU ACTUALLY MAKE SENSE AND THE CONCEPT IS SO CLEAR NOW! Thank you so much!

[@Hard_Online]

Guess u are grown now😋

[@VinUnleaded182]

thank you so much. spent hours to wrap my head around this and your video cleared this up a lot

[@ceemihail]

I've been having one of those day for 3 weeks now trying to get calculus, thx for the videos.

[@carmelamorano6296]

It’s 2020 and this is still helping people

[@oris314]

Thanks bunch! i have calculus homework on graphing derivatives with only having the graph of f(x) and didn't understand it at all. now i can actually get my homework done!

[@patrickjmt]

@agentlopez1 used to teach, but with 'only' a masters, you can not find full time university positions. only short contracts with poor pay and no insurance or benefits. so, i no longer teach, except on youtube!

[@EGabrielFulton]

You my friend, deserve a medal.

[@GoChaca]

You are the reason I am passing Calc. thank you so so much!

[@MoonMoon-bj9jr]

this man still coming clutch after 11 years

[@rachelmgosse2195]

oml a king thank you. you helped me understand and now it all clicks!!!

[@SnoopPwn09]

Here is something that helps me... start with the orignal function (f). If you see that it is increasing then the f'(x) is positive. If the original function (f) in decreasing then f'(x) is negative. Then you can repeat this for f''(x). If f'(x) is increasing, then f''(x) is positive or concave up. If f'(x) is decreasing, then f''(x) is negative or concave down. In addition, if you are looking for extemas use f'(x) and if you solving for points of inflection, use f''(x).

[@doctacool312]

watched a ton of videos and this is the first one that helped me understand how to imagine the derivative properly, thank you

[@patrickjmt]

@Ilikeroots ops, thanks for posting this, sorry it took e 3 months to notice. it is gone now : )

[@omarmartinez399]

dude, you explain this with such great clarity thank you!

[@adamdebesai]

With your explanation and teaching, who wouldn't get this? Great video!!!

[@mintbreakart]

THANK YOU SO MUCH! This is the only bit I didn't understand. And I got it immediately.

[@patrickjmt]

thats true... if i called it the 'step function' i spoke incorrectly! it does clearly 'jump around' though

[@MarzNet256]

Great video. Gave me a great refresher for the Caculus I took about 20 years ago. I've been teaching my 8 year old son how to graph simple functions (like x squared) and their derivatives. I think doing problems on a blackboard with chaulk makes math a lot more fun for kids.

[@patrickjmt]

@ashley92193 no problem, come back any time :)

[@safar127]

I WAS SO LOST BUT U MADE ME FIND MY WAY AGAIN THANKS!!!

[@patrickjmt]

glad i could help you out :)

[@vivian164]

OMFG THANK YOU

[@rzehrahayder7788]

honestly thank you, seriously needed this

[@LeonardNdegwazugzwang]

You have THE best vids in calculus THANKS

[@delahkful]

i just love you so much, i've always had miss understanding on this.

[@lillyslone5474]

This helped me more than my calculus teacher ever has

[@coyotes2012]

Your videos always give me a good refresh for my college calculus class. Thank you VERY much for these videos. Helpful and to the point

[@Qasso124]

almost 10 years, I come here yearly to make sure I remember how to sketch the derivative of graphs :|

[@syn586]

You were really helpful man. Really.Thankyou. And no your sketching isn't that bad.

[@bobnoodle420]

You are better than my calc teacher why am I paying her exactly??? Thank you so much!

[@sunlitmoss]

this was so helpful you just saved my ap calc grade

[@animemewmew7]

Thank you Patrick :) You are helping me to understand and relearn (better, this time) calculus before my AP exam next Tuesday.

[@mblackops2]

catsithkellas I'm taking AP Calc rn. I'm thinking about dropping out. Is it worth it? School has started for like a month now and I have a D in the class. I got an F on my quiz and on my test.

[@audaciousifti]

Thanks for the help, you explained this really fast and easy and helped me with my homework and test study.

[@defycool]

Thankyou, this is going to save my life for tomorrow's test!

[@kldodo]

u know what, i have been studying from u a lot , it's like you are my professor :) lol, I appreciate it !

[@patrickjmt]

@lethaltimes i will make a video of this in the morning; i am done for today : )

[@patrickjmt]

because the slopes of the tangent lines are constant over those intervals

[@Ri-gr6vh]

You literally just saved my life

[@yuhoseok47]

you are such an awesome teacher. Thank you I really appreciate