what's a derivative?

source code: github.com/skearya/derivatives
this video was made completely with motioncanvas.io/, a code to animated video library
notes:
- the ball did not fall for 3 seconds i lied, it was actually around 2.5
- you might see delta X written as h
- derivatives are often shown as f'(x) or dy/dx (d is Δ (delta)'s infinitesimally small cousin)
0:00 physics example
1:34 rate of change
4:22 instantaneous rate of change
6:42 derivative application

[@Th3Curs3dChild]

*Testing conducted in an environment where Earth is 40% lighter than our world

[@skeary1666]

had to make the numbers simple somehow :)

[@Th3Curs3dChild]

@@skeary1666 Metric:

[@Faroshkas]

How did you even make these animations? They look seriously good. Also, the explanation was top-notch. It gave me fresh perspective on how to go about explaining this subject. Congratulations!

[@skeary1666]

thank you! i used motion canvas ( motioncanvas.io/ ), the documentation is very good and their discord is helpful :)

[@Canying_ylia]

@@skeary1666I’d love to work with you on a video, If you’re interested hmu!

[@Canying_ylia]

@@skeary1666Hey dude, I’d love to make a video with you, if you’re interested, hmu!

[@Sebastian12339]

This is one of the best explanations I've found on derivatives, thanks!

[@Oxygenationatom]

This is an change of pace for your channel lol. I love it

[@lilypad429]

His channel experienced greater "rate of change" than most channels did😅

[@Oxygenationatom]

@@lilypad429literally and figuratively

[@isavenewspapers8890]

@@OxygenationatomFiguratively?

[@Oxygenationatom]

@@isavenewspapers8890 like his channel overall

[@isavenewspapers8890]

@@Oxygenationatom I was just confused because "figuratively" implies the usage of terms in a way outside of their actual meaning, but I don't see how that applies here.

[@angelamilani6961]

Nice! I really enjoyed the animations!

[@NockaMama]

Well explained, I still don’t get it but very well explained!

[@theabhinavtales5815]

Therefore your cognitive ability is Is very low

[@kaeez]

I love the production.

[@pixelatedparcel]

Beautifully explained!

[@jakob8409]

Very well explained and visualised

[@caroid9093]

This is what I was trying to understand for hours yesterday and trying to visualise the concept of a derivative , and literally got this in my feed today

[@bucketmann3443]

Very well explained. The animation gives off Veritasium vibes.

[@samueldeandrade8535]

Ve ... Veritasium? Does he use animations???

[@zperm6462]

@@samueldeandrade8535 no, no he doesn't

[@samueldeandrade8535]

@@zperm6462 yeah, that's what I thought. Thanks.

[@augustsanchezdunn628]

More like three blue one brown

[@zperm6462]

@@augustsanchezdunn628 facts

[@redye5858]

Underrated, thanks

Hello, is there anyway to contact you? 😊

[@skeary1666]

yes, my discord username is "squisket"

@@skeary1666 I just added ^^ markgandhi

[@kenfrank2730]

Excellent job with the graphics. It makes learning easy and fun. And it looks pretty cool.

[@bobtheblob2770]

So a tangency for a non-constant radius spline?

[@michaelhassey2709]

Cheers. Well done.

[@internetandcomputerprobe4426]

Really informative please continue on limits , derivatives , and others also.. >>>

[@anunnakiiscomming9810]

well said

[@valentinleguizamon9957]

this is so good!! I loved that you displayed the function at the right by making space and didn't take out the graph!! Everything is on point, I learned with calmness, thanks a lot Skeary!!!

[@acemany]

It's a good video, I liked it

[@bruhifysbackup]

explained extremely simply. this is just pure brilliance! btw, what font do you use for the equations? This font looks clean asf

[@skeary1666]

thank you, its the default LaTeX font, "Computer Modern"

[@submergedgems9955]

Need more math and calculus videos!!!!

[@fern8580]

To bring us joy, could you do the same thing again(with explanation) highlighting the speed of increase of 1 kg of gold or 1 ounce of gold between 2021 and 2024 in order to see if the increase in price is in acceleration,or if stagnation begins to appear? link "Gold Price Charts & Historical Data" Best regards from a new subscriber !

[@bentobottega]

Nice video, but check you audio. Your voice is popping. You can solve it with some audio software or just putting a sock around you microphone.

[@alexandrugurgu7126]

Chintesența ingineriei! 😢

[@mocha6686]

video :3

[@zandbergx9747]

I don't know, sorry

[@user-uq6po8dv6i]

"shtraight line down" lol?

[@SilverSurfer33]

Isn't speed just distance/time you don't need a derivative for that I still don't understand how they work

[@hontom11]

you're right, but the derivative is for speed at a single point (rather than an interval of time) where both distance and time are 0, making that division impossible. that's why we use a limit in the derivative

[@samueldeandrade8535]

Hahahahahajahajahaja. There are actually two speeds: average and instantaneous. Derivative is the instantaneous speed. Do you get it?

[@MuffinsAPlenty]

Imagine you're driving a car. As you go throughout your route, sometimes you will speed up, and sometimes you will slow down. When you're done with your trip, you can find the total distance you traveled (read it off the odometer, for instance) and divide it by the amount of time the trip took. And you will get a speed. But that will be your average speed, not your instantaneous speed. What taking (total distance)/(total time) gives you is a speed, but it's not your speed at any one given point. Instead, it gives you a speed that, if you had been constantly traveling at that single speed without every changing speed, you would travel the same distance in the same time. So that's why it's an average speed. It averages out all of the speeds your were traveling at any given moment. Let's say your average speed is 40 mph. But there were times during your trip where you could look down at the speedometer and see speeds like 30 mph or other times when maybe you had speeds of 50 mph. Those are instantaneous speeds. They're the speeds of "right now". Real-time speeds. That's what the derivative captures.