What is a derivative?
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- เผยแพร่เมื่อ 25 ส.ค. 2024
- What is a derivative? Learn what a derivative is, how to find the derivative using the difference quotient, and how to use the derivative to find the equation of the tangent line. This is a free math video tutorial by Mario's Math Tutoring.
0:11 What is a Derivative
1:22 Finding the Slope Between 2 Points on a Curve
2:05 Difference Between the Average Rate of Change and the Instantaneous Rate of Change
2:34 Using Limits to Find the Instantaneous Rate of Change
3:15 What is the Difference Quotient
3:23 Notation for the Derivative
3:46 Example 1 Finding the Derivative of f(x)=x^2 Using Difference Quotient
5:02 Using the Derivative to Find the Slope at a Point
5:26 Writing the Equation of the Tangent Line at a Point
6:00 Example 2 f(x)=x^3 - 4x Finding the Derivative to Find the Relative Maximum and Minimums
7:40 Using the Difference Quotient to find the Derivative
7:57 Using the Binomial Expansion Theorem to Simplify
8:54 Setting the Derivative to Zero to Find Turning Points
9:35 Graphing the Polynomial With the Turning Points
10:07 Summary of What the Deriviative is, How to Find it, and How to Use It
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![The Derivative in Calculus Defined as a Limit - [1-2]](http://i.ytimg.com/vi/9boavjdulxY/mqdefault.jpg)
If you would like to see another video I did on finding the derivative using the difference quotient click here: th-cam.com/video/x8j-4WYLM6Y/w-d-xo.html
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Good on you Mario. I have been studying lots of videos about differentiation, and finally with your tutoring, I understand what I was having trouble with. Thank-you. ☺️
Within the first minute, you taught me more than my college level calculus class has ever. I still dont know wtf I am doing. I just know to follow the steps and somehow I get to the correct answer. I had no clue wtf a derivative even was, only told to find it. Thank you for explaining something that a college level course just expects of me.
facts school likes to over complicate things till the point your brain is overwelmed and just blocks out all new information as useless
this is the best video by far i have found on derivatives thank you sir !
You’re welcome! Glad my video helped you understand derivatives better!
I agree
Thanks Kim! Glad you liked the video!
I came here just for a refresher. Ended up having a better understanding than before.
Glad my video helped you Ricky!
Thanks, Professor X, godspeed.
You did such a good job explaining this. I've seen so many cal students understand how to do the math but have no understanding of the actual concepts behind it.
Glad you liked my explanation of what a derivative is.
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This is where I learned what a derivative was. Nobody ever explained it to me in one definition well enough.
“A derivative is the formula for the slope of the tangent line” “The average rate of change is the secant line between x2 and x1”, which is where limits can come in. This is crazy helpful!
You sir, listen, I didn't even have to watch the whole video, you nailed it very quickly in less than 3 minutes. I was looking for a video I can use to help someone understand derivative, this video ended up helping me much better instead, job well done Sir, in less than 3 minutes. There a bunch of videos here just hitting around the bush and ending up with no real definition of derivative.
Thank you
You’re welcome mashuli! Glad you liked my straight to the point video about what derivatives are!
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You explained in eleven minute video what other tutors struggle to explain in one hour videos and still leave students confused. Thanks.
My son does not like to do the dirty work of researching and learning things so for time to time I help him by watching your videos. I must tell you that you are one hell of a teacher. You explain things very easily. Thank you so much.
I had to study how to do derivatives, but it always mostly just memorization and I never understood what was going on under the hood of all those power rules, product rules etc.
This is the FIRST time I ever understood where it all came from, like what's the actual math under the hood! Thank you so much for your videos on this topic!
You’re welcome! Glad my video helped you break the code on derivatives!
Hey, there. This is a Doctor of Musical Arts who hasn’t taken more than 12 credits of STEM courses in his entire secondary education. I haven’t taken a single math course since an algebra review class in community college in ‘05, and no science courses since an Acoustics for Non-Majors course offered for Music students in ‘09.
Of course I used some very basic knowledge of science somewhat in my grad level courses, but my main point is that I’m not especially educated in this area. I’ve never taken Calculus, nor Pre-Cal, nor even Trig. I barely remember high school geometry.
This video helped me get a significantly better understanding of the basic mathematical use of derivatives in an abstract sense. Some of the algebra was a bit fast for me, but I understood somewhere between 85 - 90% of what was discussed here.
I’m pursuing this because I’ve always had a conceptual interest in physics, especially quantum physics and general relativity. PBS Spacetime and similar channels helped feed my interest, but I felt I lacked any understanding of even the basics of the equations.
Channels like this are helping me continue my education in mathematics so I can better enjoy Newtonian, Lagrangian, and Hamiltonian mechanics, so I can better comprehend the reasons why certain quantum phenomena are expressed they way they are by the math, or how the energy needed to accelerate mass to c approaches infinity. Thanks so much for this excellent resource!
This is probably the best derivative explanation I have watched. Thank you so much sir.
You’re welcome Wilhelm! Glad you liked my video!
Never thought the sword demon will study the derivatives XDD
Can we just take a minute to respect this guy's amazing ability to legibly write/draw on a whiteboard
I always learn concepts like these but my professors never actually explain them as a concept, they only talk about the formula and how to use it to solve problems. This makes math really boring because you have no idea what you're actually doing. Learning HOW and WHY stuff works in math makes it 100x more fun.
I learned more by the discussion about the tangent line than I have in four weeks of daily two hour classes.
I went from being completely lost in calculus to understanding the how and why with just this one little video. Thank you sooooo much!
Your English is really perfect Sir! I got what derivative is. Thank you Sir
You’re welcome! Glad my derivative video helped you!
Online class is a struggle for me who has experience this kind of set up for the first time. Thank you so much for this video, sir! It's so clear and precise.
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I just spent the last semester in college algebra wondering what the point of all the f(x+h) and fog was. I also wondered for the entire year how exactly you find relative max and minimas of turning points. This video just connected so many dots for me, thank you!
You’re welcome! Glad it helped!
I watched this video so many times, such that each time I watch it, I discover another aspect not previously seen.
Glad you liked the video Norman!
After rereading and rereading the textbook and watching multiple videos ive found the one that actually teaches what I need
Glad my video helped you Marc!
Even after purchasing a textbook of my own- Calculus for Dummies, my understanding is less than expected.
You are one of the very mature mathematicians i know. Thank you for your conscientiousness!!!
Glad to see Jhonny Sins back as a teacher. Can't wait for your next class! 🥰️
Ha. I had the same thought.
Took me till halfway thru the video to understand since I haven't taken pre-calc yet. But this is the only explanation that I could understand on TH-cam. Thanks for this wonderful video!
Wow okay thank you. I came to this video because while I could find the derivitive I had no idea of what I was actually finding and needed this information to understand how exactly the math works. Thanks A Ton!
You’re welcome James!
Thanks, I find that understanding the concept behind something makes doing math problems so much more logical. I'm loving my AP calculus class so far!
Sir you are Amazing ! you know why you are amazing? because you make thing so simple.. why something is so ... and you explain it so simply.. thanks so much.
Awesome! Glad you are liking my videos and my channel Zadran!
Thank you! You explained it very well. I understood everything, even as an 8th grader.
Glad it helped!
I've been studying this topic for years now but this is the first time that I have genuinely understood the nature of a derivative. Thank u Professor X!
I had no idea why I was finding derivatives or how they were used, and this made EVERYTHING make sense. Thank you so much for this video explanation!
I'm so glad!
If I were really good with math I would have created a time machine... Then I would have went back in time and got my younger self to meet you and learn math from you and then I would be better at math. Then we would have met as two professors in an alternative time line of our lives and we would have been great friends teaching math to people who don't have a time machine. I also have ADHD so this was what I thought of after watching your video. Thanks!
Definitely the best math tutoring channel on Earth!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
it's the second video I watched for you, I feel like you've done some magic for me to fully understand the idea, you're really great sir! thanks a lot.
You’re welcome Basil! Glad my videos have been able to help you!
By far the best video I’ve seen about derivatives. Thank you
Glad you liked the video Callum!
This video is really good, now I understand what a derivative is and does
Thank you sir!!. I knew you are a real teacher aside from being a doctor, plumber, a soldier and an astronaut.
Derivative of x^2 is 2x , same as nx^(n-1), now i know where it came from. Thanks sir mario.
You’re welcome Walter!
They used to teach us in school this way: whenever we tell you the derivative of 5x^2 you answer 10x. Without knowing where it came from, we'd never advance and understand real maths.
Glad my video helped you understand the origin of those shortcuts for finding the derivative!
@@MariosMathTutoring Can you please make a new category of videos about how to revise maths and how to be more familiar with it? It'll be an awesome gesture from such a great teacher.
Excellent video for understanding the concept, I haven't done it before and watched and learned the entire thing without writing a single number down. That said, there were two sticking points for me. First was that I got lost when you started doing the derivative for x^2 as I had no idea where the input for h was coming from. After doing it you pointed out that h approaching zero means h=0 though. Second was after doing the square root to get +/- 1.15, you stuck it right back into the function equation but didn't say that it was the point we were looking for until later, so I spent awhile trying to understand that too.
Overall 10/10 video, maybe that feedback will make a future one 11/10. Thanks a lot.
Best video hands down! You saved me.... mostly in this pandemic. Thanks teacher
AWESOME explanation Mr. Mario - Thank you very much !
Best video for Deriviatives available on TH-cam.
Just a request as well as suggestion Professor: Please write a little larger in size, it will make contents visible efficiently.
Otherwise you just nailed it.
Loved it.
Thanks Ishaan!
Thank you very much for posting the helpful videos, and your videos are alway in my consideration of wtching whenever I am stuggling for math problems.
Thank you very much for the demonstration, I was struggling to figure out what a derivative actually meant before watching this video.
Glad it helped!
Thank you so much! Concepts like this beat being shown formulas with no explanation any day.
Best english video about derivatives
Sir, you are a magician, lots of love, respect and dawah from Bangladesh.
So nice of you!
The increment of the function can also be expressed through the difference of functions, using the factor k-->1: d(f(x))= f(kx)-f(x). Similarly, the increment of the argument: dx=kx-x.
Then d(f(x))/dx=lim[k-->1] (f(kx)-f(x))/(kx-x)
Thank you very much, I have an exam tomorrow and this helped me very much. I have finally grabbed the concept of derivative
I would say that HE has been the best teacher for me so far!! Appreciate you man!
This video helped me understand why we need to use derivative in ML, Thanks great job
Glad it helped!
Thank you! It finally makes sense!
You’re welcome Jaret!
Thank you Mario, for the concise and thorough review!
Thank you so much! I had difficulty understanding derivatives but this video came to the rescue
That is too clear to not understand derivatives. Thank You!
Currently writing a bullsh*t essay about derivatives and this video helped a lot, thanks Mario!
Perfect - thank you. This is much better than written text books for sure
Thank you very much sir, your follower from Iraq. Very useful video thanks much.
You’re welcome Ali!
i share your calm with the topic - fantastic style of sharing the knowledge
you are talking so clearly. you are a gift teacher
Glad you like my teaching Jack!
@@MariosMathTutoring I am confused about sin cos function using π π /2， is that degree or Radian， because I know determineing the minimal or maximum point in sin cos function we should use π/2 to define left side or right side of this function
AWEsome dude. boy. thanks to YOU. i FINALLY got it in Plain English very well explained. thank YOU SO much. !!!!
Glad it helped!
What a beautiful explanation, I really like what u did with the graph thing, very insightful and very resourceful.
Really helps me a lot! Thank you!
You’re welcome Shane! Glad my video helped you!
This video helped me understand derivatives better! Thank you Sir.
Thank you so much for this video.
You’re welcome!
great explanation
Thanks sir for explaining what it is
i really hate it when teacher teach me how to do it before teaching me what it is
Glad my video helped you Mustafa!
Thank you for the explanation! It was clear and coherent
You’re welcome!
Superb explanation !! thanks
Thank you sir it was a great help
You’re welcome Rosa! Glad my video helped you!
your voice is really clear, thank you
You’re welcome! Glad you liked the video!
Very nicely explained sir
Wow!!! Thank you sir
I dropped out of calc. I found it so boring, unintuitive, and unexciting- whereas previously I loved math.
This video impacted me so much it physiologically made me excited for math again. I could feel endorphins in my chest just thinking about it. I guess I just had the wrong teacher. That or the fact I'm way more interested in physics now, perhaps I'm seeing it's usefulness in a new way.
Glad to hear it inspired you and got you reignited about math!
thanks for this great explanation
Your welcome! Glad it helped!
Thanks
Amazing explanation
I was so confused until the end. A derivative is basically just a substitution in order to find a specific point like a max or min.
great respect . The way you teach but please one thing put the definitions for us and the different symbols of derivitives ill be waiting for you please and thanks a lot .
This is truly a mind blowing video, I was struggling with the concept of derivatives but now it all makes sense! Thank you!
You’re welcome! Glad my video helped you!
I LOVE YOUUU SO MUCH, PROFESSORR
I wish you worked at my college :'(
Thant you for all your videos Mr Marios .It helped me a lot to understand what Derivatives is !!!
You’re welcome! Glad my videos have helped you!
10/10 video, thanks!
Amazing job explaining everything!! Thank you!!
Great video. Love the explanation of why this is useful.
Thanks Mr. Clean
God why mathematics is that beautiful ? thank you professor ❤
You are very welcome
Really helpful explanation. Thanks for this, much appreciated.
Where were in my +1, +2 Sir Superb video...😃
Thank you for the explanation sir! It helped me a lot.
miraculous explanation, can't be more satisfied !
Mario Sir is the best....
Glad you like my videos Muhammad!
Excellent Video. Great Explanation!
Very very very helpful
nicely explained
Great vid. Got a real-world application of the use of a derivative? It can be computed, but so what? What do I do with it?
Thank you sir,it was wonderful explanation
excellent video! 🏆
This Tutor is still the best in 2023😇
Loved it a lot 💕💕
Thank you very much. These videos help.
Glad to hear that!
amazing explanation.thank you
Glad it was helpful!