The definition of a derivative

⚠️DISCLAIMER⚠️: This is not real celebrity audio/video. All video and speech was generated to help others learn about maths, physics, and engineering.

[justacoolname]

The brainrot got so bad it flip around and turned into braingrow

[copperII_]

why am i learning everything through brainrots now...

interesting...

[hellxapo]

The person who created this is a modern genius

[penguenosss]

No joke, I passed differential calculus in college without knowing this. Our teacher only gave us the formulas without further explanation. This video sure helped a lot to answer a few questions, thanks!

[Secretname]

It’s not really about as close as you can to 0 as humanly possible, it’s as close as you can get to 0 as inhumanly possible

[cybrlol]

I can't believe I ACTUALLY learned something out of this, this is surprisingly well explained

[holdupsomethingaintright]

What an elegant answer, explained through memes.

[malldvd]

Here I am, procrastinating for my calc final, and then this pops up. 😅

[MeghGireesh]

I’ve been learning this for nearly two weeks and this video made me understand it better than anything my professor has taught me💀

[RRR]

Its crazy how many really fundamental concepts I am just beginning to appreciate from these videos almost a decade after passing calc 3 in college with flying colours. Is there anyone else who didn't know that derivatives are actually limits lol. Please don't stop making these!

[adriangenera]

This is the smartest thing you will see in yt shorts

[BigSmoke-dpyh]

ive watched tons of videos explaining calculus and still struggled until now, thanks man.

[ItsLtime]

It means that it applies anywhere, since slopes remain constant only for linear polynomial functions. Because in a Quadratic Polynomial function for example, as you get the higher, the rate change increases. Therefore we cannot have a singular value to define the rate of change(slope). Hence we cannot use the secant line. We then use the slope of the tangent line(or a point that only intersects the function at once). As we get the points closer, the distance approaches zero. So if we get the closest to zero we possible can, the distance becomes practically the same across all input values. Hence the limit!

[Hyvexx]

I don't know whether to laugh or to cry at the fact that I fully understand why the formal definition of a derivative f(x+h) - f(x) /h. The entire school year, I just memorized it because I thought it was an arbitrary formula some guy found.

[nathanbarnes]

Differentiation from First Principles doesn’t need to be complicated, when explained like this it’s very easy to understand

[hakamal-asyam]

please continue bro, you're the best, this help me alot

[rohithnambiar]

This is the best explanation of derivative by far

[eshan]

Man for the first time, I literally got to know about the exact details of this formula, thank you so much man.

[homosapien]

I just realized why it’s not some arbitrary point in the middle of the two. The second x value is literally defined as the first + a distance h. If you make that distance infinitesimally small, you get closer and closer to the first x value. So you have to be describing the slope, or instant rate of change, of the first x value.

[unknowm]

this is the best visual representation of derivative that ive seen by far and all of a sudden i understand why the derivative formula is like that now.