Q10, second derivative of an ellipse, by using implicit differentiation

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So you think you can take the derivative, handout here: https://blackpenredpen.com/calc1 Second derivative with implicit differentiation! An ellipse. Please subscribe and share my videos to help my channel grow! 😃 Comment #YAY down below & your comment might be featured in my future videos!!! My simple setup: 😃 https://youtu.be/IKk7k-CMttE , Check out my site & social media 😃 www.blackpenredpen.com 😃 [email protected] 😃 https://twitter.com/blackpenredpen 😃 https://www.instagram.com/blackpenredpen/ Thank you for watching! blackpenredpen | 曹老師

25 Comments

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

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  • Cool

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

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  • I got d^3y / dx^3 = -2187x / y^5 Edit: forgot the x

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  • Awesome!

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  • 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)?

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

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  • 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

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  • sin (8x) =??

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  • Please make video on partitions..

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  • Nice trick at the end! By the way, this would be something cool to do a video on: https://math.stackexchange.com/questions/903481/nth-derivative-of-fx-using-limit-definition

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  • #YAY

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

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  • 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.

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  • 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)

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

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  • That blows my mind that ellipse has no inflection points!

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  • This channel is fire

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  • Daily learning a lot. Thanks for being so consistent.

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  • man high school seens so boring when i start seeing calc

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

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

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

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  • I got: (-9y^2 - 81x)/y^3

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  • #YAY!

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