AP Calc
posted by Sanya .
I need to find the second derivative for this:
2x^23y^2=4
I understand all the steps but for some reason I get the wrong numerator. I get
(6y^4x^2)/9y^3
The answer is 8/9y^3

You did just fine and your second derivative is correct, if you meant (6y^2  4x^2)/(9y^3)
except they took it a bit further.
notice your numerator is
4x^2 + 6y^2
from the original
2x^2  3y^2 = 4 , then
4x^2  6y^2 = 8 , and
4x^2 + 6y^2 = 8
to get their 8/9y^3
If you were marked "wrong", then that is bad,
when differentiating implicitly, there are often multiple variations of the same answer.
Here is a way to check if two possible answers are equivalent:
Pick any point which satisfies the original equation, sub that point into the two variations of the derivatives, you should get the same answer if they are equivalent.
e.g.
the point (√8,2) is on the original curve
y''  your answer  = (24  32)/72 = 8/72 = 1/9
y''  their answer = 8/72 = 1/9
ok, then !!