Parametric vs. Cartesian (vid#4): Second derivative d^2y/dx^2

How to find second derivative, d^2y/dx^2, of parametric curves?
Second derivative notation explained.

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blackpenredpen | 曹老師

[chandankar]

I left two days for holiday and this man have completed 7 videos on parametric forms.Hats off

[quahntasy]

VId 4 came before vid 3. I think the third one is on its way.

[ZelForShort]

Now do the same for Snap Crackle and Pop

[ThePharphis]

I don't know how I got a math minor without ever learning why it was d2y/dx2 but I'm very grateful for having learned it now. The notation always seemed so weird and at the end of the day I guess it's due to laziness

[alejandrofabiangarcia]

You are the best teacher I have seen(I speak spanish)...
I am studying university, 2 weeks ago I was showing to class parametrics derivatives and I did the mistake you teach to not do :'v You had to upload the video before my lord😂

[-ck]

False; dx^2 is different than d^2x.
Edit:
I was right. Also, videos #1, #2, #4?! What is next? #8?

[rickpala_]

i always treated the “d” as a prefix meaning change, similar to “delta x”. except, d implies that the change is so small it’s practically zero.

[emperorpingusmathchannel]

Video 2 was so good that it doesn't need video 3 following.

[IMIGamerz]

First-time like. First comment. Haven't yet seen full video but I hope it's informative and awesome.

[antimatter]

The mystery of video #3. Coming to you next episode.

[bagui]

Can you learn us how do you switch back and red pen with one hand?

[MrMuscia]

Great video! Can anyone explain why dividing d^2y/dx^2 by (dx/dt)^2 does not yield an equivalent equation? The algebra of the differentials still leads to d^2y/dx^2

[fedefex]

Great Video! Can you make a video where you speak about "old calculus", so dx d^2x as infinitesimal object? Why here i can't find d^2y, and (dx)^2 separately function of t and then divide them?

[chaosredefined]

But is there a function such that (d2y/dt2)/(d2x/dt2) = d2y/dx2?

Also, alternate method:
d2y/dx2 = (dx/dt * d2y/dt2 - dy/dt * d2x/dt2) / (dx/dt)^2 (Quotient rule applied to finding the derivate of (dy/dt)/(dx/dt) )

[silasrodrigues]

" d2y/d2x "What does that mean? Norhing? Something never used and with unknown and misterious powers?

[ochirbatnyamsuren]

Just recently taught this in different way - through Peano derivatives and differentials. Differentials are different, in respect of x or t. Then no such confusion arise. However good try.

[dwaraganathanrengasamy]

I am gonna say
Because it doesnt look so.
So interseting to see what's gonna be.

[husklyman]

Vid 4?
not 3?
Oh the answer is false

[yaleng]

Looks like true, but I bet 10 euros for false.