The Tangent Line and the Derivative (Calculus)

In calculus, you’ll often hear “The derivative is the slope of the tangent line.” But what is a tangent line? The definition is trickier than you might think.
Tangent lines are important because they are the best way to approximate a curve using a line. We can then use the slope of the line as a way to measure the “slope” of the curve.
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Written and Produced by Michael Harrison
Michael Harrison received his BS in math from Caltech, and his MS from the University of Washington where he studied algebraic number theory. After teaching math for a few years, Michael worked in finance both as a developer and a quantitative analyst (quant). He then worked at Google as a software engineer for over 5 years before leaving to found Socratica.
You can follow Michael on Twitter: / mlh496
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[@q_q123]

Great explanation. Calculus is fun when you actually know what's going on

[@sabashakeel0369]

Yeah mostly we don't know what are we doing 😂😂

[@bloomsxobini]

Realest coment

[@Siawash777]

My Calc professor taught the same way but his way was too complicated that I got lost lol. That’s why I am really happy someone did it this simple

[@mallorysmith1820]

I love how you went over misconceptions of what a tangent line was first before giving the definition of it. Great video. :-)

[@pinklady7184]

Exactly.

[@arthurandrews113]

That’s why math and other complicated topics lose people over time. We are given over simplified explanations which eventually fail us. Instead we should be taught the most accurate understanding. It may be harder to grasp initially, but when it is, will be worth the effort.

[@rafaelrincon3109]

"If you don't mind, I'd like to on a tangent and touch on an important point." lol

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i love the effort you put to make the audience understand the concept of tangent crystal clear.

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[@bartlx]

I was going to make a video on the subject myself, until I saw this one... The fact that most definitions just talk about this tangent line touching the curve at 'one' point never really satisfied my hunger when looking at graphs. Great explanation, visuals and presentation pace.

[@slackbabo3858]

I really like how you gave examples and then invited the viewer to try to come up with their own definition for a tangent line first. Hopefully you release some new math videos soon. Keep it up!

[@petej011]

Thank you so much. The definitions with visuals made the Tangent Line and the Derivative easier to understand and appreciate.

[@sureshc4759]

thanks a ton for the awesome explanations and for making the videos available on UA-cam

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This is amazing, it made me understand the maths we take at school at a deeper level. Now it makes much more sense to me, thank you!

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I just want to point out the sound design, I've never seen an educational video pay attention that. It was amazing

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This is so helpful and clear.it really saved me half and hour reading the textbook!

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Squeaky clean explanation with succinct live demonstrations. Perfect teaching method!

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Best explanation in UA-cam. Made things so detailed and easy to understand. More such videos please. Thanks

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greatest teacher I've encountered on UA-cam. thank you so much

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Great vids. I really hope you don't stop making them. Specially next semester that I'm starting calculus

[@Socratica]

Thanks! We'll be making *many* more Calculus videos in the coming months.

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where is the calc 3 and linear alegbra ones..

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Verry Verry good videos.
Thanks to Socratica team..........

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WOW! This is incredibly well done.

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A clear and comprehensive explanation enhanced with an extraordinarily good use of graphics.

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Sir, your class is far above excellent.

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WE GOT ONE!!!
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I love how it's so clear to understand!!

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This is so well explained. Thank you :D !

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great video format , encourages the viewer to think, it's like a game , so creative , really really loved it

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One subscribe from India. Really your explanation are amazing.

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You really answer all my freaking questions about tangent line
Thanks and I'll promote your video

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very easily and neatly explained. Thanks

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I love it! It's a crystal clear !

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Sir, you may not believe that I have already thought of it in my school life. Thanks for this wonderful video. You really deserves like and subscribe.

[@ahlalkubur]

This is amazing... Best explanation for tangent lines I have watched so far...

[@Socratica]

You're so kind, thank you for saying this! It really encourages us to make more videos.

[@Ihasgun]

I think this is the greatest explanation of a tangent line to a curve I've seen so far

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thank you! This Video was fabulous

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Thanks A lot for making all my concepts clear!

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Amusing,I really wanted such a video from somedays.I think it is the better channel for learning the fundamental....

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check out the
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We are so glad you are visiting us from Egypt! We dream of visiting one day! Thank you for watching and for your kind message. :)

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The best ever explaination of derivatives. Absolute perfection.❤❤❤

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Great work! Thanks a lot ✨

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Finally best channel to learn Mathematics. Keep adding more advance topics..........

[@SuHAibLOL]

I really love calculus and I understand the concepts, but as I teach the concepts to others, I wonder how it can be put best. This is likely the best video I've seen on introducing tangent lines and it was a great watch. Keep it up man!

[@samikakar2353]

sir , you have conceptually explained it very well ,hope you will upload more videos

[@Theviswanath57]

This is awesome, the best I saw on this

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Thank you so much for the great explanation !! I will have an exam after two weeks, and needed this clarification!!

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Woah bro, u're such a legend at explaining.. plus the visual video is really super helpful ❤💙❤

[@YasirKhan-bl8lj]

Awesome! you made it simpler

[@johnhammer8668]

Thanks very much. Such an awesom video.

[@olivewang961]

It's amazing to see how to get deeper and deeper to the definition of tangent! Remind me how little I know about first principal😂

[@artofemong6148]

Great explanation I love it mas clear pa sa clear

[@amandeepsaha]

thankyou
it helped me a lot

[@michellethapa3247]

Thank u so much ♥️
Finally got what derivative and tangent line is

[@omaryarali7805]

Perfect explanation👌

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It makes a better approaching to understand concept better

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Very Good Explanation.....

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Explained Superbly..

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Quality stuff!

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Thanks so much Sir , first time, I am capable to understand what calculus actually is . Literally you gives understandable content and helping a lot of students.

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Excellent!

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I wish that my first college math class explained it this way. Nice job!

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thank you!

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We're so glad you're watching, Emily!! :D

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Great videos! Could i ask you guys something? Could you gives us more of a basis on math talking about Analytical Geometry and René Descartes? Thanks

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Marvelous!

[@qualquan]

Leibniz the co-founder of calculus gave the correct definition of a tangent line ie it touches a curve at 2 adjacent points separated by dx in the x direction and dy in the y direction, so it is dy/dx = the derivative or the hypotenuse of a right triangle = (dy^2+dx^2)^1/2
this avoids division by zero.
a single point cannot determine the direction of the tangent but dy/dx does

[@epuremath]

Avoids division by zero, but needs monads, which havnt been developed until middle of 20 century and overcomplicated, good replacement...

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Thanks a lot!

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very nice > thank you

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It will help more.

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keep up your good work!

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thank you

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Animations are amazing.

[@otakurocklee]

Very nice. Great video. The truth is that the derivative gives the definition of tangent line, not the other way around. For pedagogy purposes I think it's fine to tell students that the derivative is the slope of the tangent... as a way to get start since students start with some kind of intuitive "feeling" of tangent.
But the idea that derivative is "defined" to be the slope of the tangent is a misconception. The derivative is what it is. The tangent is defined as the line going through a point on the curve with the derivative of the curve at that point as its slope.

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Extrardinary explaination

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Please More Videos .... And Please let me know what is the software you use to get those animation of equation

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[@zacktrever1878]

Dx/dy 4 lyfe