Visual derivative of x squared

A visual of the derivative of f(x)=x squared. We show how to think about the derivative of a function visually.

#manim #calculus #derivatives #derivative #tangentline #slope #parabola #mathvideo #mathshorts #math #visualmath #graph #parabola #linearapproximation

[kirahen]

I'm 14 and I haven't yet done calculus, but I hope this explanation will come in handy when I finally get to it

[chilldo]

Another interesting way to see it, is that if you look at the intervals between the perfect squares (1, 4, 9, 16, 25...), you can see that the intervals are 3, 5, 7, 9... The odd numbers! And the odd numbers are represented as 2x+1. But we will leave the 1, because of derivative rules which I cannot explain because I don't know it myself too much.

[lastoneleftmedia]

If teachers taught like this instead of teaching us "tricks" to solve the equations, it would not have taken me 30 years to finally understand derivatives.

[hiimgamerspruzzino]

Sometimes all we need is a very simple explanation. I've been studying derivatives at school since the last few weeks and couldn't really understand them deeply. Thank you so much!

[sumithadavid]

I was searching this explanation for nearly 2years and now I understood
Thank you so much, 😊😊😊😊😊😊😊😊😊😊😊😊

[izzabelladogalini]

Excellent graphic representation of derivatives

[Aditya_]

Basically most people forget the essence of derivatives....
Derivative means rate of change over a small interval ( very small : dx )
So imagine a square with sides x its area is x² now if u increase its dimensions from x to x + dx its area is x² + 2x*dx + dx²
This means its area increased by 2x*dx + dx² .... Now this change with respect to that small interval dx means the expression 2x*dx + dx² / dx = 2x + dx
Since dx is very small ( ) we ignore it
So d ( x² ) / dx = 2x

[karthikteal]

I learnt that 13 years ago
I understood the meaning today

[eymedjt]

The most underrated math channel, what i've seen. Now i can explane how to woks derivates for myself.

[itsnotshakespeareitsdennis]

Omg! How beautiful is this presentation!!!!

[timgabby]

Nice job. Visuals are so helpful. Curious old UK duffer here :)

[fpskiller]

Thank you so much. i always need such type of explanation.

[ssaamil]

In love with the visuals, what program is this? Amazing explaination too :>

[mahamamjad]

I really want to know how is that -7.82 and 1 came . And you said is we compute slope of the function along the curve but that would be an How do we get those points that you plot in the below

[srikrishnaghosh]

Man! you are going to kill the imagination of young calculus lerners😅 jokes apart, we had to visualise this same idea in our mind only, and now kids will learn it easily. Beginners will find this very helpful and will use their time to think about something more abstract ❤ i am going to use it as a teaching material 🎉🎉🎉🎉🎉thanks for sharing.❤

[gnvuwnt]

What software do you use to play with those graphs? Pretty Neat and also easier to understand the concepts.

[asparkdeity]

Good intuition for people who’ve never come across calculus yet (especially the kids)

[NumbToons]

Dude, I have this video/visualisation recorded in my mind (i mean before watching your video)

[SebastianRodriguez-rkvx]

I’m five minutes into learning derivatives and this has taught me more than any teacher

[NECTOMIC]

Finally I have known what is a derivative