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.
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 !!
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