Calculus Made EASY! Understanding the definition of the derivative

[@张小雨-w1g]

Best explanation on this topic I have ever seen! More students need to see this

[@jimmycstephens]

Thanks!

[@drjitutoring]

Thank you!

[@sg2664]

I’ve watched A LOT of math videos and this was by far the best explanation of the first derivative. Your communication skills and presentation materials are top notch. I’m super impressed. Any thoughts on creating a statistics class that incorporates R?

[@drjitutoring]

Thanks! I greatly appreciate your kind words! As for statistical computing with R... I'd have to learn that first myself as it is not in the area of my specialty. Is that something you're familiar with?

[@sg2664]

I have just started to learn R -- my first programming language. It’s an incredibly powerful tool. I think you’d enjoy it. I keep rewatching your videos. You are talented. Keep up the great work. It will pay off big for you, and in the meantime know that you are helping lots of people and that they appreciate you.

[@Jenny7603339]

Great job

[@Jeiideezee]

Best explanation! Thank you so much for the video! Can you make a video about limits? (Delta-epsilon proof)

[@drjitutoring]

Thank you! And sure, I will include a video on Delta-epsilon proof when I do limits (by end of this week).

[@syri_bigbrother.]

Thank You very much Sir , best explanation ever !!

[@mentanagavenkatasrinivas9245]

very beautiful and elegant explanation!!

[@drjitutoring]

Many thanks!

[@dark3l192]

Thank you so much, my teacher didn't explained derivatives this clear. he directly moved on questions but because of you now this topic makes a lot sense to me, Thank you again! please make more videos about math

[@drjitutoring]

Will do. My plan is to make as many Calculus videos as possible over the course of this month. Thanks for your support!

[@gautamroychoudhury2735]

You explain very well. Thanks a lot. Regards

[@drjitutoring]

Thank you so much!

[@Thecarshow-ry9cq]

just wow, this is the best explanation. thankyou

[@sreedhar75perupally]

Mr Dr Ji 🙏 Sir your explanation is the Best of the Best. Extraordinary Detailed Explanation. I Salute You. One thing is Sure that your explanation can't be understood by those who don't have Strong Fundamental Knowledge of Algebra & Co-ordinate Geometry. ❤❤❤❤❤ 🌟🌟🌟🌟🌟

[@alesianakipava7781]

Dr Li, I’m so thankful that I met your video. That’s incredible ❤

[@drjitutoring]

Thank you! I'm glad you enjoyed the video.

[@asapstudies1934]

as a math tutor ..I aprove this explanation>>>

[@drjitutoring]

😁✌🏻

[@MeerimayBakytbek]

Wow 🤩good job 👍🏻

[@drjitutoring]

Thank you!

[@StudywithmeinPakistan]

Greatest video ever on this topic. Regards from Pakistan 🇵🇰

[@drjitutoring]

Thank you! Means a lot :)

[@chamindasilva5917]

Hi! A secant is a line that intersects a curve at a minimum of two distinct points,whereas a tangent line is defined as the unique line that touches a curve at only one point so a secant line will never look like a tangent line therefore the differentiation never gives us actual slope of a curve.

[@Thecarshow-ry9cq]

This is the best explanation , i understand it finnaly , and please make another video explaning how the integration is related to the concept of Limit ? Thank you for your efforts , you are making history and changing the lives of many , thankyou

[@StudywithmeinPakistan]

Sir you have covered everything, but if you can also make a video on derivatives of log and exponents, that is missing, otherwise your work is all complete.

[@alext8828]

At 3:28, y is defined in terms of x. That makes no sense unless the student is reminded that the definition of y is f(x). So when someone asks what (x,y) is equal to, the answer can be (x,f(x)). Let's make it more clear. [ x, f(x) ], because the y is actually, by definition, f(x). I think that's a stumbling point for some students because things start looking crazy at that point. Great video.

[@drjitutoring]

Yep, included that just for precisely that purpose!

[@alext8828]

@@drjitutoring You're the best. Thank you for your attentiveness.

[@lolobee313]

How are you getting that answer when you simplify the numerator at 09:55

[@dfparker2002]

At the 10m mark, what is the thought process behind "simplifying" the numerator)? Is the helpful substitution random or procedural?

[@drjitutoring]

Great question! The substitution I made into the bracket is completely random, I even considered just putting (......) but I felt it looked ab it weird. But factoring out the "h" on the numerator is 100% procedural. You should be able to factor out the "h" after simplifying the numerator every single time. You can see the actual procedure of simplifying the numerator at around the 10:50 mark

[@deepakkumar2078]

Great ! If we are getting slope after one time derivative, then what we get if we do it third time, fourth and soon.

[@drjitutoring]

We’re basically just finding the slope of the previous function. Which seems pointless - but let’s say in the context of kinematic, the derivative/slope of the position vs time graph is the velocity graph..but if we derive the velocity graph then the slope of the velocity graph gives us acceleration. Differentiating the acceleration vs time graph gives us the jerk..etc

[@theghosttiger1446]

Dr. Ji! So it's like fine tuning a radio on am to get a clear station?😮

[@jsswan1]

This was so well done. I saw a months old post of yours saying you were going to be posting “every day”. What happened? I think students would *really* get a ton of value from more calculus videos that would cover the span of subject matter from at least a basic course (Calculus I).

[@drjitutoring]

Thank you! Honestly there were a lot of factors but now I'm back and will be uploading videos as often as I can. As I get better with editing and animation I hope I can be as often as once per day, but for now at the very worst it will be 3-4 videos per week. After my next few videos that I have lined up, I will be focusing on completing Calc 1, starting with limits. Thanks again for your support! Really appreciate it.

[@jsswan1]

I really look forward to more Calc videos. I don’t find a bio of you anywhere. I am curious how you came to be Dr. Ji! I hope there will be a bio forthcoming along with videos.

[@jan-willemreens9010]

... Good day Dr. Ji, After watching your excellent presentation on the definition of the derivative I don't think there's any teacher left who could explain this topic better (lol) ... however, every time I see the formula f'(x) = lim(h -> 0)[ f(x + h) - f(x) / h ], I personally think it's a shame that the denominator is referred to as only " h " , instead of " (x + h) - x " , after all, you lose a lot of valuable information right from the beginning, which means being less creative when solving for instance limits; especially for people still in the learning process ... f'(x) = lim(h -> 0)[ f(x + h) - f(x) / (x + h) - x ] is much more clear to me, and I observe this too with tutoring students ... thanking you for your more than clear to the point presentation ... best regards, Jan-W

[@drjitutoring]

Agreed! And after reading your comment I wish I stayed at that portion of the equation a bit longer and explained it, before simplifying it to just h in the denominator. I hope by explaining the slope equation in the video, the students can see the flow of how the equation gets simplified to just h in the denominator!

[@jan-willemreens9010]

@@drjitutoring... Thank you for your clear reply Dr. Ji. I just want to show you via a very basic and simple example what I meant by " a loss of valuable information ... " ... Given: F(X) = SQRT(X) ... applying the Definition of the Derivative to find F'(X) ... F'(X) = LIM(H -> 0)[ SQRT(X + H) - SQRT(X) / H ] ... of course we can use the Conjugate method to rewrite the indeterminate limit form in such a way that we can finally plug in 0 for H, but suppose we had started with the form ... F'(X) = LIM(H -> 0)[ SQRT(X + H) - SQRT(X) / (X + H) - X ] , we would also observe an alternative solution strategy, namely ... treating the denominator (X + H) - X as a Difference of Squares as follows .... [ SQRT(X + H) - SQRT(X) ][ SQRT(X + H) + SQRT(X) ] ... cancelling the common factor [ SQRT(X + H) - SQRT(X) ] of top and bottom , to obtain a limit form, which is solvable ... F'(X) = LIM(H -> 0)[ 1 / SQRT(X + H) + SQRT(X) ] = 1 / 2*SQRT(X) ... I hope I made my point a bit more clear to the interested people ... when treating the original denominator with respect, we get additional alternative solution paths in return (lol) .... thank you again Dr. Ji and best regards, Jan-W

[@kenesu1281]

💖✨👌🏻

[@josephajoseph9535]

But why we plug in h to zero in the equation (xh+4x) if it only approaches zero?

[@drjitutoring]

Great question! It is the fundamental idea of limits, which isn't covered heavily in this video. I will post another video dedicated to limits. To answer your question, the idea of differential calculus is to focus on dynamic change rather than static number. For example, instead of a point with coordinates (2,3), in limits we try to see the behavior of the curve as the x-value approaches 2 (which means the y value should approach 3). This might seem redundant if we already know a point exists at (2,3), but it could be very useful if we don't have such coordinates! In that case, when our x approaches 2 and we know our y value approaches 3, then the limit as x --> 2 would be 3, even if there is no point/data there at all. As you can see, this is a great loophole we use for the definition of the derivative. Our h cannot be 0, but it would be great to see what would happen as it approaches 0. So by plugging 0 into h, we're finding a limit (aka what we "think" should exist there), even though nothing actually exists there. Hope that made sense?

[@josephajoseph9535]

2 points doesn't become infinitely closer.. I guess

[@medicisounds1384]

At minute 4:30 i was SCREAMING. Why THE FCK DID MY PROFESSOR NOT EXPLAIN THIS. I'm in college now and lazy ass professor couldn't explain this??? FOH