second derivative of an ellipse, by using implicit differentiation

second derivative of an ellipse, by using implicit differentiation, calculus 1 tutorial

[danielburgoa]

I really like this channel, thanks for the latest videos, I'm learning a lot.

[perveilov]

I never knew that you can reuse the equation from the earlier despite how many times you've differentiate it from the original. Thank you for the new info

[joluju]

Very interesting calculation. It's also interesting to graphically check the results.

[MrAlexioor]

Could You make a video about graphical and general meaning of deratives of curves like elipses, circles etc? In fact I have in mind all no-function relations where we use implicit differentiation)

[quahntasy]

Daily learning a lot. Thanks for being so consistent.

[witchlightsands]

Thank you so much ! this really helped me, I couldn't figure out how to simplify it :)

[marcushendriksen]

Paused at 5:50: wow, the numerator has the original ellipse in it! Which means it must never change. Also, does this mean that the value of the second derivative is completely independent of x? (going by the fact that the numerator can be rewritten as -81, and there's only y in the denominator.) Will keep watching to find out!

[garyward]

According to algebraic manipulation of the first equation, y = SQRT(9-9x^2). Couldn't the y^3 in the denominator be replaced by (9-9x^2)^(3/2)?

[tommax]

Blackpenredpen, could you please make a video on how to convert absolute value functions to piecewise functions?

[aarn]

Doing a bit of mental math, I think that the general formula for the second derivative of a eclipse (ax^2 + by^2 = r) is -ar/(b^2 y^3). Though this was all in my head, so I could've slipped up somewhere.

[hollow]

Can we conclude that the second derivative of kx^2+y^2=k is equal to -k^2/y^3

[stapler]

So as long as my y-coordinate is not zero, I can calculate the acceleration for an object moving in an elliptical orbit. :)

[francis]

For d^3y/dx^3 I got -2187x/(y^5) or -27/(y(1-x^2)^2).

[simpletn]

Okay so second derivative done. Time to do third :)

[Theacbsmith]

You have the 2nd derivative in terms of x but then have an answer in terms of y? Arent you supposed to do the inverse???

[patrickgleason]

That blows my mind that ellipse has no inflection points!

[eterno]

Could you not have solved the problem using partial derivatives? and why not?

[MagnusSkiptonLLC]

I got d^3y / dx^3 = -2187x / y^5

Edit: forgot the x

[jaap]

how is the grafic of this second derivative ? (sorry if my english is bad)

[naturelover]

How many mic do you have ..my sir..😊😊😊