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

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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[jonathanlaliberte]

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.

[mariakhan]

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 ?


😂😂😂

[benjisurf]

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

[josuequintero-tdgh]

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

[boss]

Is this going to appear on GCSEs 2018/19 ?

[alanfate]

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

[orenugaadebayo]

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

[meaarts]

Why doesn't my teacher teach like this 😭

[davidoliveros]

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

[johnnolen]

@ 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.