Second derivatives (implicit equations): find expression | AP Calculus AB | Khan Academy

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Given an implicit equation in x and y, finding the expression for the second derivative of y with respect to x.
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[@jonathanlaliberte3175]

Khan Academy, a youtube channel explaining better than my University teacher I pay hundreds dollars per trimester Thank you very much !

[@firettoYT]

If you simplified the last thing by using a common denominator, you could plug y^2-x^2 back into the derivative to get 4/y^3. Much cleaner.

[@ADOBY_RTV]

I was about to say that but i found u good job

[@OgieCruzshowbizwatcher]

korek final answer 4/Y^3

[@benjisurf]

forgot how good khan academy was, this made it click for me after a long time ur the goat

[@josuequintero-td5gh]

I'm taking calculus II and I finally understand implicit differentiation after working with parametric equations

[@mariakhan6090]

3:06 Sal: well that is just going to be one times the "other thing" Fancy y adorned with -1 exponent by Sal : Am I a joke to you ? 😂😂😂

[@LenchoGemeda-lh9gy]

Tnks bro

[@cringekid8435]

You are a god, good sir

[@boss4078]

Is this going to appear on GCSEs 2018/19 ?

[@haroonq2456]

Not 2nd derivatives

[@johnnolen8338]

@ 4:36 "And we are done ..." Technically that's true if you don't bother to simplify your result. However, adding the fractions together over a common denominator, and substituting 4 for the expression in the numerator yields y" = 4/y^3.

[@euphoriaashoor7348]

Thank you so mutch sir.

[@alanfate4853]

Why do you have to move dy/dx to one side to find d^2y/dx^2?

[@nikethmandadi9795]

awesome thank you

[@meaarts4972]

Why doesn't my teacher teach like this 😭

[@orenugaadebayo8859]

What if I use quotient rule instead of product rule that you used, would I still get the same answer? Cause I actually used quotient rule, but what I got is totally different from yours. I got a y-x/y^2

[@sandeshsulgaonkar3091]

You would get the same, you might have an error in your calc

[@bipinmaurya3824]

Best video

[@nawarahilal3337]

I Love you

[@davidoliveros7497]

Wouldn’t it be easier to use the quotient rule ??

[@johnnolen8338]

It's certainly no more difficult to use the quotient rule here but a lot of folks can't remember the quotient rule. Solving the problem the way Sal did, illustrates the fact that the quotient rule is actually a special case of the product rule.

[@spurti]

@@johnnolen8338 indeed

[@spurti]

@@johnnolen8338 I have solved with the quotient rule and the answer is same that is: (y^2-x^2)/y^3

[@johnnolen8338]

@@spurti I'm a pragmatist when it comes to calculus. Use whatever technique will get you the right answer. Good luck with your studies. 😃

[@spurti]

@@johnnolen8338 thanks for advice!! now I will use sal's method cuz its intuitive and I hate memorizing formulas.

[@slimevlogs7556]

First

[@1rushabh]

Anyone else got 1/(1+y) ?

[@MinDetonator96]

I'm the 69th like on this video

[@ft.ludacris5650]

First