Calculus 1 Lecture 2.1: Introduction to the Derivative of a Function

[@AirIndy1]

Professor Leoanard, You did every college kid a favor by posting these lectures. You made Calculus fun, and way easier to learn. I used these videos for review before my midterm. Salute!

[@kidd1941]

I've got midterms next week😥

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Yeah sadly this is so true, so many people feel and choose to end their life because they are struggling in college and begin feeling hopeless. If more professors made an effort to not let students fall into the margins and instead taught methodically, checking if the class is following, in a style similar to Professor Leonard, many of those students would have alot more hope.

[@starzredweb]

what is the derivative of the function of his bicep curve

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[@7906jun]

= undifferentiable (muscle level off the numeric chart known to mankind).

[@cconnie3762]

It's over 9000 lol.

[@Neme112]

His sharp peaks would obviously not be differentiable.

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[@hawahardy]

0:00 - Concept of Derivative 5:41 - Finding derivative of f(x)=2x²- 3 and the equation of the tangent line to f(x) at (2,5) 16:00 - Eg. Find derivative for f(x)=2x³-x 27:45 - Eg, Find derivative for f(x)=3x+2 30:10 - Eg. Derivative for f(x)= sqrt (x) and equation of the tangent line at x=4 41:00 - Instantaneous velocity 43:16 - Eg. S(T)= 1250 - 16T² 57:25 - Differentiability 1:11:30 - Representations for derivatives

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This guy makes calculus look so easy. When I took calculus1 7 years ago, the professor never mentioned calculus is for solving slopes on a curve or finding the area between 2 points in a curve. He was more concern about making us recreate all the formulas we used in class from scratch.

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when Professor Leonard asks if everyone understood the problem and you raise your hand :)

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"exactly hhhh or when he says : are we alright with this? and you be like" i'm might actually pass this isn't just alright this is perfect

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Same!

[@jerrymahone335]

why doesn't he teach the sun and power rule off the bat. all of this could be avoided.

[@geromeponch6248]

Same

[@seanwells1672]

Because the power rule isn't introduced till later chapters and some teachers won't let you use it till you've learned the def. of the derivative function

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I have found your lectures on youtube and since I am an electrical engineer major at USF, I have found your lectures on here more beneficial than the ones I sit in on a daily basis. I wanted to thank you for posting your lectures. I just wish you actually were a professor at USF so I could benefit more from an actual sit-in lecture

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I am in the same boat! A software engineering major and unfortunately my profs are pretty bad. They are not clear and concise and my calc prof has terrible handwriting which I can never read. I pretty much only go to class to know what kind of questions he puts emphasis on for tests, I usually have to spend a few hours teaching myself everything. Thankful to people like professor Leonard.

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Not to sound condescending, but how did you even get into EEng without knowing this stuff? I did my B.Eng in mechatronics and then M.Eng in electrical (research was in the field of photonics). I would of been crucified if I wasn't extremely proficient in at least calc 1 in my first year, it was all assumed knowledge from day 1.

[@peachlife5118]

Well personally for me, I did very well in this stuff in high school but I had a large gap between graduating and college and I definitely did not do any math during those 4 years (woops). Lol so thankfully it is all coming back to me through watching these videos. The only really new concepts I have to learn are incorporating log, ln and the trig functions into differentiation.

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Experiences in life vary. Not all universities are ran like a chop shop. Additionally, leading with "Not to sound (anything)" only amplifies that (anything) you are trying to avoid.

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you explain everything so clearly. watched every video. i dont even need to go to my lectures anymore!

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At the moment, I'm a graduate student but I never understood calculus during my undergrad. A few weeks ago I was telling a friend in grad school that I needed to enroll for undergrad calculus and he recommended that I follow professor Leonard's lessons on youtube. I started watching from lesson 0.1 and I feel like professor Leonard just empowered me. Thank you so much prof, you just made my life easier and because of you I am well equipped to understand and relate better to both science and math.

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Milo Still probably because of Professor Leonard’s muscles... :) *Gym as in fitness/workout place :)

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The absolute best calculus professor I have ever seen! I wanted a summer refresher with Calculus 1 from AP Calc in high school before I continue with my calculus classes... I DID NOT KNOW HOW MANY CONCEPTS I DID NOT ACTUALLY UNDERSTAND THE MEANING OF WHAT I WAS DOING. Professor Leonard makes you understand why you're doing what you're doing. I will use his videos even while I'm taking calculus the next two semesters.

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[@zongonative7397]

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Thank you sir! I got lost a little when my professor started to explain derivatives. After watching your video a few times, I felt very comfortable. I went to class today and was not lost at all, I followed EVERYTHING. Thanks again. You are definitely, THE MAN!

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Thank you for posting these videos! I can finally grasp the concepts of the derivative with your examples and explanations. You're a teacher who actually teaches! Thank you!

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PROF I am watching your lecture from Kenya ... You are inspirational to me... calculus is becoming easy easier and easiest through you... keep up the spirit you are so helpful to all students world wide like me.... I wish you many years to come to help many

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idk if this is a good strategy but basically my teacher just reads off of the textbook (yes even in an online class) and since I don't understand anything, I make notes of the textbook as I go along and then when my exam is near, I BINGE WATCH the lectures I need. but frl these videos are not only informative they're also fun cuz it's in a classroom setting and prof leonard is dynamic in his way of teaching so watching these 1-2 hour videos don't even feel like a chore. I actually FEEL like i'm learning.

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Apparently in 2012

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universalpaper 6 yrs ago

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ive always loved math and im even a math major however, when i took calc 1 for the first time i hated it... the professor didnt teach well and her exams were 10x harder than the examples on her study guide and on her quizzes. im taking it again and my new prof also sucks at teaching and has even admitted that he didnt like his job... im almost thinking of changing majors but if anyone can convince me to stick it through and actually learn this stuff it'll be u Superman

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+Sveva Ramasco hahahha adesso sto studiando per il mio esame di Calculo, veramente i professori fanno schifo, tutto lo ho imparato da qua

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Thank you SOOOO much! I'm taking calculus in University and this is so helpful! Please don't stop!

[@millermiller3439]

I felt the need to post this comment. I stopped doing work for calc during week 2 of college. I'm now at week 7 and am cramming as hard as I can to save the course. You have been beyond a life saver. P.S. Don't do this. Just do the work from the start lol

[@AtaAriser]

We had our calculus midterm this week and I killed the limit thanks to you L-King! Now I'm rolling with you on the Derivative and will on Integral, when I see them questions I easily fended 'em off with the things you taught, limit has ended, lol

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Thank youuuu I get excited when I pause the video, solve the problem before you do it and then I see that I got it right :) I am good to go for my exam

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Love your videos, it's helping me get back into calculus after a major life event that forced me to drop out of college. Love the jokes and humor as well. I just wanted to point out a fun fact lol. You said "differentiability" was a great Scrabble word. Well really it's not because no word longer than 15 letters can ever be played in a game of Scrabble when following the rules 😆

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idk how his students focus... im distracted looking at his beauty

[@hummathwiz5713]

I’ve finally got to understand what those math symbols really mean in derivatives. Thank you so much!

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You are the master of this game Prof Leonard

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Thumbs up!!!!!!!!!!!! Your tutorials are all i need in my calculus class......

[@Varde1234]

It's really hard wanting to find the derivative using limits when you already know the d/dx trick. It's so much easier. Derivative of a constant = 0; derivative of X is just 1; derivative of e^x is just e^x; derivative of x^2 (all you have to do is just move the the exponent to the front of d/dx and subtract the exponent n-1) is 2x. Although using limits for this enriches the understanding, it's so inefficient for questions like find the derivative (2(x^2))-3.

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[@ins4rt_username18]

4:38 I didnt understand what this formula is for such a long time, until I found this video. Now I finally understand it!!

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The GOAT calculus teacher🔥

[@jimmidge13]

Howdy Must admit to failing Calculus in 1951 first time around and only wish you were my instr. You are good

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Jim Midgley are you still alive ?? Not being funny but wow 1951 ?? You must have been born in the early 30s . You’re almost to the point of being in the “greatest gen “ I think

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Doubt you will see this Professor, but I wish you had a pdf of practice problems for every section! Or at least problem numbers for every section from a recommended book! Love this and reviewing calc 1 to calc 2 to prep for calc 3. Hoping to finish up to calculus 3 by summer so I can be ready.

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best teacher on this planet!!!

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Those videos really helped me sir I appreciate that you're videos really helped me I was lost and I don't know what to do but once I saw your videos sir I did all the questions right from the textbook thank you so much😍😍😍👌🏻👌🏻👏🏻👏🏻

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Thank you very much professor Leonard. Don't give up good work. Wish you all the best sir.

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29:08 slope of a curve at any point is not at all a constant, but a fixed equation in which x can be substituted

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Thank you so much for explaining this rollercoaster. It's hard and a long process to answer one question. 🤓

[@SparshKarki]

You're Awesome. You take everything to root level so everything is understandable. (y). I hope there are other videos on derivatives.

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the vid is gr8.now i think maths is all about fun rather than numbers....

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Thanks a lot professor Leonard. I wanted to know what was exactly the meaning of the Derivative.

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