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Second derivatives (parametric functions) | Advanced derivatives | AP Calculus BC | Khan Academy

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Sal finds the second derivative of the function defined by the parametric equations x=3e__ and y=3__-1.
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Опубликовано:

21 авг 2024

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Комментарии : 25

@TheCaptain14 8 лет назад

The second derivative doesn't seem intuitive at first, glad I watched this video as a refresher.

@BluFFiNMuFFiN87 8 лет назад

You're a life saver Saul :') thank you sooooo much!

@satyamtiwari4974 3 года назад

Your writing through mouse is much much better than my handwriting😅

@arbitrary_inquiry 8 месяцев назад

was so concerned that sal wasn't going to put that three in front of e.

@user-df2ml7ys2e Месяц назад

really helpful, Thank you!!!

@s3gu1n 8 месяцев назад

The answer is not 1/(12e^t) it's 12/(e^t) because 12 is not to the power of -1 only e^t is.

@AnkitPlayzMC Месяц назад

Are you dumb?

@darpmosh6601 6 лет назад

Hello Mr. Khan, I just have a question: why is the second derivative set up like ((d^2)y/(dx^2)) instead of something like dy^2/dx^2

@dariopl8664 5 лет назад

hello, if it's still useful. When you got the first derivative of "y" you wrote d(y)/dx, now you're taking the derivative of dy/dx. Then its notation is d(dy/dx)/dx = d^2/dx^2, "d^2" because you've got two "d" symbols which are multiplying on one another and "dx^2" because there is a "dx" two times.

@letsgetiton99 4 года назад

@@dariopl8664 thank you sir

@Honestboy918 3 месяца назад

Thanks sir

@davidcarmichael644 6 лет назад

You're awesome bro..... Thank u !!!! So much

@dipankar-kumar-singh 4 года назад

Thanku very much

@yangliu3754 6 лет назад

Very good explanation. Thanks.

@nichlaus 5 лет назад

thanks so much

@brookejohnson7828 7 лет назад

Bless your soul!

@fourthhorndeservesrats7584 4 года назад

him saying “i encourage you to pause the video and think about it” at 3:51 was lowkey passive aggressive

@Iamme-rk7ki 4 года назад

Thank youuuu sirrrrrr

@anon3550 4 года назад

Wow glad i watched it, else i would have never known why we use that equation for Second derivatives of parametric functions....my teacher just told me to mug up the equation

@sergey_zatsepin 7 лет назад

Well, I don't understand why we need to divide on dx/dt, and not just take the second derivative of dy/dx

@Kay-dx8vm 7 лет назад

i know, right ? I'm trying to understand that part too

@plasmasheep4098 5 лет назад

not sure I understand your question but when you take the second derivative, you take d/dx of dy/dx, giving you d^2y/dx^2. however you can't take the d/dx of a function that is written in terms of t immediately, it doesn't make sense to take the derivative with respect to x when the function only has t. In order to conquer that obstacle, we convert d/dx to d/dt / dx/dt. Now this part of the equation is in terms of t, and the derivative can be taken. I know its too late but jic anyone has the same question