Visual Derivative Definition!

This video animates the idea behind the derivative of a function. We show how to think about the definition of the derivative of a function visually by using a limiting process of slopes of secant lines to obtain the slope of the tangent line (which measures the instant rate of change of a function at a point).

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

[xdgqmpe]

The best explanation! I like how you explained the reason why we use limits. I wish I saw this video earlier

[supermarioenthusiast]

Beautiful visuals man! Is there also a possibility for you to do this demonstration but with x->a replaced with the h->0 where h represents height proof for derivatives?

[SaiManognyaDesetty-bsgp]

I properly understood what a derivative is after two years of learning calculus. Same goes for why limits are necessary. Thank you very much for this short and highly informative video!

[MoguMogu]

Back when these videos to me were gibberish now make me realize how much easier I would've had it if I had studied calculus by trying to understand the math instead of trying to force myself to do the math problems.

[suwkodm]

Best explanation on YouTube please upload the entire video of calculas...Your explanation is really

[jarige]

I simply love your channel, it reminds me why math is beautiful!

[Inspirator_AG]

*Step 1:* Construct a tangent line at (a, f(a)).
*Step 2:* Construct a right triangle whose base is 1, and whose hypotenuse is on the tangent line. (Ideally at (a, f(a)).)
*Step 3:* Measure the height of that right triangle; that should be f'(a).

[anandtewani]

Where the hell was this creator when I was needed the most 😢

Btw I completed my school 14 years ago.
Anyways I wished I would have got the exposure to such informative videos earlier...life would have been definitely different today.

[robertwaremusic]

I can't tell you how many videos I watched on this topic that were like 10 minutes long and confusing as hell, and this tiny video made it make sense.

[qenrl]

Your explanation make it so easy to understand! Literally only have introductory knowledge and limits and you still managed to do it. Only thing im confused about is why would you need to find the instantaneous rate of change?

[annahlee]

this youtube short was amazing for review. Thank you!

[treybell]

I wish I could love this video bc you don’t know how much this changed my perspective

[vigneshbalaji]

Nice explanation. Derivative is based on secant line

[ceebad]

Can you do something similar but for the fundamental theorem of calculus? Thank you, your videos have helped me a lot ❤️.

[antotot]

please please please please, do this with the limit definition i need it!
Thank you for your work, is super helpful

[AmanKumar-wdhm]

YouTube without distraction videos 🗿🗿🗿🗿

[jonathanreynolds]

Holy fucking cow biscuits! I've been struggling with this exact thing the last few days and I finally get it!

[wyboo]

this is great for functions between one-dimensional vector spaces, but i prefer the interpretation of "how a small movement in the input spaces changes the output space" interpretation to generalize to multi-dimensional spaces

[TalSzor]

My HS physics teacher used the same visual idea when he taught us derivatives for the first time.

[ygyigyc]

Thank you so much it really helped a lot😊